MLwiN FAQs

• Can I use the tutorial /Lemma version of MLwiN to practice loading my own data (in SPSS) into MLwiN, or do I need the full version for this?
  • Data input and output for the teaching version of MLwiN is limited to specially marked MLwiN worksheets, so you will not be able to load your SPSS files using this version.

• We are currently re-designing our network, which means that our MLwiN users will have to access the data MLwiN uses through a Citrix-"window" and they will not be allowed to put the data onto their local hard disk. This means that MLwiN cannot run on their computers but must reside in the secure network, and either be processed on the Citrix-server/Citrix-desktop, or running on a dedicated application-server.
  • We do not have a Citrix system here to test MLwiN on, so cannot give a definitive answer, however we have had reports of people using MLwiN successfully on this and similar systems. MLwiN 2.10 should have more success that previous versions as it no longer attempts to write files temporarily to its program directory.
    
    One thing to note is that MLwiN loads the whole data set being analysed into memory, so if your users are running models on large data sets on the same machine you may run into memory issues.
    
    Running more complex models can also be quite CPU intensive. Whether this is an issue for you will depend on the number of processors in your server machine and the number of simultaneous MLwiN users. Each instance of MLwiN can only make use of a single processor, so as long as the number of copies running a model is less than or equal to the number of processors in the machine there should be no slowdown compared with running it on the user's machine.

• I'm attempting to open a new worksheet directly from .dta (STATA) format and I get the error message "Duplicate name(RSTA)."
  • This error message will be produced if there are two variables with the same name in the Stata file you are trying to open. Note that MLwiN does not distinguish between small and capital letters, so for example variable1, Variable1 and VARIABLE1 will all be considered the same name. Inside Stata, change the names of any variables that MLwiN would consider to be the same, save your worksheet and try importing into MLwiN again.
    • Is it possible that MLwiN has problems reading underscores ("__")? For example, reading ___ABC the same as ABC ? 
      • No, MLwiN should count '__ABC' and 'ABC' as different. To test whether MLwiN considers 2 names to be the same, open MLwiN without opening any worksheet (you can do this via the Programs menu, via a shortcut, or by clicking on MLwiN in its folder in your Program files, or alternatively you can double click on an MLwiN worksheet to bring MLwiN up and then select New worksheet from the File menu to close the worksheet). From the Data manipulation menu select Names. In the window that appears, highlight any row and click the Edit name button. Type in one of the names you want to test. Highlight a different row, press the Edit name button again and type in the other name. If MLwiN considers these 2 names the same you will get an error message saying 'duplicate name(NAME)' (confusingly when you press OK it appears that the variable has been given the name you chose in spite of the error message, but if you press the refresh button in the top left corner of the Names window you will see that in fact the variable has reverted to its previous name). If MLwiN considers the names to be different you will get no error message. You can delete the variables (highlight the rows and press the Delete button at the top of the Names window) and test another pair of names, or you can leave the variables and name more variables one at a time to test whether a name is the same as any that you have already used.

• I'm trying to export data sets from MLwiN into files that have an ASCII file format (or .csv or SPSS data files). Selecting the ASCII text file output from the File menu command allows me to specify a column range c1-c10 and an output file name (and destination). But the resultant text file has the first 5 variables. I'm not sure what happened to the remaining 5 variables? Even entering in the variables separately c1 c2 c3 c4 c5  c6 … did not yield any better results. I have tried this process across several data files and on numerous occasions.
  • Although it appears that only 5 variables are being exported when you use the ASCII text file output window from the File menu, in fact all 10 are exported. However you only see 5 columns of data because when you export more than 5 columns MLwiN wraps the data (see section 2 of Getting data out of MLwiN). So if you export the 10 variables in the tutorial dataset supplied with MLwiN, for example, then in the exported data the first number in your first column of data is the first entry of the variable school but the second number in your first column of data is the first entry of the variable girl. The third number in your first column is the second entry of school and the fourth number is the second entry of girl and so on. This wrapping is less obvious in the case when the number of variables you export is a multiple of 5 than it is in the example given in the Getting data out of MLwiN page because when the number of variables is a multiple of 5, there will be no gaps in the five columns of output data.
    
    There are two solutions to this problem. The simplest is to upgrade from MLwiN 2.02 to MLwiN 2.1. The upgrade is free to anyone who already has a copy of MLwiN 2.02). You may find when using this version that you get 10 columns of data when using the ASCII text file output window to output 10 variables, i.e. MLwiN is no longer wrapping output data when outputting more than 5 variables. But in any case there are easier ways to output from this version, which are described in the section Getting data out of MLwiN 2.1. Alternatively, if you do not wish to upgrade, the other solution is to follow the advice in section 2 of Getting data out of MLwiN: export five variables at a time into Excel where you can put them together again into a worksheet.

• I'm trying to get a 2.5 million dataset from SAS into MLWiN. I've tried to use a SAS macro and also, to just export my data to a text file. When I use the macro to try to get my data into MLwiN, it says that it's "scanning data" -- it slows down at about 600,000 and stops at approximately 740,000. It doesn't stop at the same place every time! (for example, once it stopped at 733,800 and once at 759,700). I tried to increase the worksheet size to 50,000 and when I did, it stopped at 642,600. An error message pops up in a window: EXE file has encountered a problem and needs to close. We are sorry for the inconvenience. When I just try to import the text file, the same error message pops up. Wondering if you have any thoughts?!
  • I would suggest importing a subset of your data, eg, a random sub sample of your higher level units. Even if you manage to get all the data in all but the simplest models would take a very long time to converge. A side benefit of using a sub-sample of data will be that you can check that you haven't overfit your model to your sub-sample of data by testing the final model on alternative sub-samples of the data. When model building you will want a considerably small sub-sample of your data, say 25,000 if the model is not too complex you can then estimate your final model on say 250,000.

• I am doing 2-level logistic modeling using MLwiN. My data has >250,000 individuals within >700 clusters. I have less than 10 covariates.
  • Try using a random sub-sample of your data. With only 2 levels, 700 level 2 units and 10 covariates you do not need nearly as many as 250000 observations to get precise estimates. You will be able to work a lot more quickly with a smaller sample and therefore be able to explore more avenues and potential models etc
    • Basically, it doesn't work for the whole data on MLwiN (even single level logistic) although it works for a subset smaller data (about 5000). I don't realize any problems for importing the entire whole data.
      • You can check whether the entire dataset has been imported properly by comparing the summary statistics: are they the same in MLwiN as in your other stats package?
        • Errors: There are three types of errors. One shows me 'out of memory'. And the 2nd one shows me 'no sufficient worksheet size. The 3rd one is that MLwiN is just crashed and turn off. I have two questions. 1)can MLwiN handle such a huge data?
        • Yes. But depends of course on the spec of your computer. See faq
          • 2)How to re-configure/specify worksheet size from the 'option'?
            • Go to options worksheet then increase worksheet size to a large amount (experiment)

• I got an error message that said 'Insufficient space to run model. Increase worksheet size to at least 10000k (offs)'. How do I increase the worksheet size?
  • Select Worksheet... from the Options menu then type a larger number in the box next to worksheet size(k cells) and click Done. You may need to experiment to find a size that is large enough for what you are trying to do. (Note that there is a limit to the size of worksheet that MLwiN can allocate; this depends on your computer but is usually around 20,000 k cells. Also note that MLwiN can encounter problems if you make the worksheet size too much bigger than necessary).
    
    Note that resizing the worksheet will close the worksheet, so you should make sure that you have saved it, and you will have to re-open it again after resizing.

• Does MLwiN need repeated measures data to be in long or in wide format?
• MLwiN fails to open after changing the default worksheet settings
• I have a worksheet saved on a network drive that I can't open using MLwiN
• When I try to open the worksheets for the LEMMA course I get an error message
• When I double click on one of the worksheets for the LEMMA course, it opens with notepad not MLwiN
• Why has my data become corrupted?
• Where is the model fitting information stored in MLwiN?
• I got an error message 'cannot allocate rmatrix(ws)(like)'

• I have a categorical variable with 6 categories which I have entered into my model as an explanatory variable, and I want to test whether the coefficients for two of the dummy variables are significantly different from each other. How do I do this?
  • After running the model, select Intervals and tests from the Model menu. In the window that appears, select fixed (at the bottom of the window) and in the box # of functions type 1 (if it does not already say 1). In the top part of the window type a 1 in the box next to one of the dummy variables and a -1 in the box next to the other (it does not matter which way round you do this). In the box next to constant(k) type 0 (if it does not already say 0). Now press the Calc button at the bottom of the window. The box chi sq, (f-k)=0. (1df) now contains the test statistic to be compared against the distribution with 1 degree of freedom, and we can make the comparison using the Tail Areas window from the Basic Statistics menu. The null hypothesis is that there is no difference between the coefficients. (Important note: it may be necessary to resize the column in order to make sure you can see the entire number in the chi sq, (f-k)=0. (1df) box. To do this put the cursor over the column divider right at the top (in the grey row) and it should become a double arrow; you can then click and drag to resize).
    
    For example suppose that we are working with the tutorial dataset supplied with MLwiN and that we have set up in the Equations window a random intercepts model with explanatory variables standlrt and vrband (with vb1 as the reference category). Suppose we want to test whether the coefficients of vb2 and vb3 are equal. We run the model, and then select Intervals and tests from the Model menu. In the window that appears, we select fixed (at the bottom of the window) and in the box # of functions we type 1. In the top part of the window we type a 1 in the box next to fixed : vb2 and a -1 in the box next to the fixed : vb3. In the box next to constant(k) we type 0 (which is the default so may already be entered). Then we press the Calc button at the bottom of the window. We see from the box chi sq, (f-k)=0. (1df) that our test statistic is 73.879 (we check it really is 73.879 and not 273.879 or 5673.879 by resizing the column). We select Tail Areas window from the Basic Statistics menu. In the window that appears, we leave Chi Squared selected, in the Value box we type 73.879, and in the Degrees of freedom box we type 1. We press Calculate and the Output window appears giving us a probability of  (= 0.0000000000000000083055). We can thus reject the null hypothesis that there is no difference between the coefficients of vb2 and vb3 and conclude that the coefficients are significantly different from each other.
    
    An important point to note is that we put a 1 next to one of the coefficients we wish to test and a -1 next to the other. This is because the Intervals and tests window adds together everything in the column and tests whether the result is significantly different from 0. So by filling in the column in this way we are testing whether , which is equivalent to testing whether . We are testing whether there is a difference between the two coefficients as was our aim. If we instead put a 1 next to each of the coefficients we would be testing whether , which is equivalent to testing whether . We would be testing whether the coefficients had the same magnitude but opposite signs, which is not what we wanted to test.

Note that an alternative way to test whether two categories have equal coefficients is to refit the model so that one of the categories is the reference.  In that case the coefficient of the other category will be a contrast between that category and the omitted category, and the usual Z-test can be carried out.

• I have a categorical variable with 6 categories which I have entered into my model as an explanatory variable, and I want to test whether there is a significant difference between any of the coefficients for the dummy variables, or whether all the coefficients are equal. How do I do this?
  • To test whether more than 2 coefficients are equal, we use the Intervals and tests window as in the FAQ How do I test whether two coefficients are equal? We proceed as described in the answer to that question, but in the box # of functions we type the number of pairs of coefficients that we need to compare. For example, if we wanted to test whether 3 coefficients , and   are equal, we would type 2 because we need enough pairs for each coefficient to enter into at least one comparison (so for example we might compare  with and with ). If we wanted to test whether 5 coefficients were equal (as in the case of testing whether the coefficients for all dummy variables for a 6-category variable are equal) we would enter 4. In general, we enter n -1 where n is the number of coefficients we want to test.
    
    We fill out the columns that appear in the top part of the window according to the same principle as when testing whether two coefficients are equal: each column corresponds to one comparison between two coefficients, and in that column we enter a 1 in the row corresponding to one of the coefficients and a -1 in the row corresponding to the other. There are many possible ways of choosing the pairs to compare, but one way that will always work is to take the first coefficient and compare it with each of the others. Thus when comparing 3 coefficients we can compare with in the first column and with in the second column; and when comparing 5 coefficients we can compare with in the first column, with in the second column, with in the third column, and with in the fourth column. So when comparing 3 coefficients, supposing that the model consists of cons as the first explanatory variable and the 4-category explanatory variable as the only other explanatory variable, one correct way to fill in the columns (down to the constant(k) row) would be:
    
    

    Column 1	Column 2
    0	0
    1	1
    -1	0
    0	-1
    0	0

    
    and when comparing 5 coefficients (again with cons and the 6-category explanatory variable as the only explanatory variables in the model), one correct way of filling in the columns would be:
    
    

    Col1	Col2	Col3	Col4
    0	0	0	0
    1	1	1	1
    -1	0	0	0
    0	-1	0	0
    0	0	-1	0
    0	0	0	-1
    0	0	0	0

    
    If taking this approach, the 1s should all be in the same row and the -1s should form a diagonal line going downwards from left to right.
    
    As for testing whether 2 coefficients are equal, we put 0 in each column in the constant(k) row (and in any rows corresponding to other explanatory variables) and press Calc.
    
    In the chi sq, (f-k)=0. (1df) row of each column appears a test statistic which allows us to make the comparison between the particular pair of coefficients set up in that column, but the statistic we need to make our test that all the coefficients are equal is to be found near the bottom of the window where it says joint chi sq test(?df) (where the question mark will be the number of comparisons we made in the top part of the window). We can get a p-value for this test statistic using the Tail Areas window as described in the answer to How do I test whether two coefficients are equal? (remembering to input the appropriate value for Degrees of freedom, which will not now be 1). This will be the p-value for the test with null hypothesis that all the coefficients are equal; thus if the p-value is small enough we can reject this hypothesis and conclude that (at least some of) the coefficients are significantly different from each other (although there may be no significant difference between some pairs and we would probably want to investigate further to determine for which pairs there is a significant difference and for which we cannot reject the hypothesis that there is no difference).
    
    What exactly is the  test statistic that appears at the bottom of the window next to joint chi sq test (?df) and why does it test that all the coefficients are equal? This test statistic is the test statistic for making all the comparisons specified in the columns simultaneously: for example, in the test described above to compare 3 coefficients, it is the statistic for the test that AND ALSO . In other words, when we reject the null hypothesis (that both these equalities hold), this implies that there is a significant difference between  and  and/or a significant difference between  and  and/or a significant difference between  and  (at whatever level of significance we are using).   Note that last point: although none of our columns made a comparison between and , if then our null hypothesis is not true. This is because and means . If there is a significant difference between and  then it cannot simultaneously be true that and  (even though the test statistics in the chi sq, (f-k)=0. (1df) row may indicate that when we make the comparisons separately, we find there is no significant difference between  and  and that there is no significant difference between  and ). Therefore another way to describe the joint test is to say that it is a test of whether . So we can see that indeed the joint test is the test that we wanted, that tests whether all the coefficients are equal.

• V has gone negative definite
  • The V matrix for a higher level unit or block has become negative definite. This can occur when, for example, the variance function for a particular combination of explanatory variable values becomes negative. Common cases are with repeated measures models where high order polynomials are fitted or in models where the level 1 variance is fitted as a function of a continuous explanatory variable such as age. MLwiN will automatically approximate V by the nearest positive definite matrix using a singular value decomposition.
  • This problem may only occur during the course of iterations and convergence may eventually be achieved smoothly. If the problem persists and even if convergence is obtained you should carefully examine the specification of your model to see whether there is an obvious problem which can be fixed by adding or removing parameters.
• SSP matrix for fixed (random) part has gone negative definite
  • The matrix has become negative definite. This can occur in similar situations to those above and MLwiN will approximate to the nearest positive definite matrix.
• Matrix in constraint procedure has gone negative definite
  • When constraints are used, for example in cross classified models and generalised linear models, a further matrix which should be positive definite is created involving the constraint vectors and in some circumstances this can become negative definite. The matrix is approximated by the nearest positive definite matrix. Less is known about why this happens, and you should examine your model and any imposed constraints carefully.
• Random part has gone to zero - cannot continue
  • Sometimes, in complex models, all the random parameters obtain zero values during iterations. In this situation the estimation cannot continue and you will need to restart and you should look carefully at your model. This sometimes occurs because the starting values used are inappropriate.
  • Try running a simpler model than the one you wish to fit and then add further terms when convergence has been achieved. If you have already built up your model in this way try restarting with the most complex model specified.

• I (successfully) ran a multinomial model, then cleared the Equations window and set up a binomial model. When I pressed Start, I got an error message which said
  
  error while obeying batch file C:\Program Files\MLwiN v2.10\discrete\pre at line number 11: name c1180 'H' C1181 'F~(H)' C1182 'H*' C1183 'P' c1184 'MASK' c1189 'Y-VAR'
  Duplicate column name.
  • This error message occurs because when MLwiN estimates a binomial or multinomial model, it sets up some special columns in the worksheet. When it does this it gives them certain names. The names for the columns used when running a multinomial model are P, -P, H, F~(H), H*, Pi and Y-VAR, and these occupy c1178 to c1183 and c1189. When the model is cleared, these columns are not deleted. If another multinomial model is set up and run, c1178 to c1183 and c1189 get given these names again. This does not cause a problem because the same column is being given the same name. However, if instead a binomial model is set up and run, the names and locations of some of the special columns are different: H, F~(H), H*, P and Y-VAR are put in c1180 to c1183 and c1189. When MLwiN tries to give these names to these columns, it discovers that P is already the name of c1178. Since there can't be two columns with the same name, the error message is produced.
    
    To solve the problem, after you clear the Equations window simply scroll down in the Names window to find c1178 to c1189, highlight these columns and click the Delete button at the top of the window. This removes the contents of the columns and renames them c1178, c1179, and so on. When you set up and run the binomial model MLwiN is then able to properly create the special columns it needs.
    
    Note that the same problem does not occur if you try to run a multinomial model after having run a binomial model. This is because, although c1183 is already named P when MLwiN tries to name c1178 P, c1183 is being given a new name in the same command, and so c1178 is successfully named P without there being 2 columns with the same name.

• I tried to set up and run a binomial model using a macro, but got the error message 'Variables random at bottom level should not be used in model'
  • It sounds as though you have included a command in your macro like this:
    
    setv 1 'cons'
    
    and this is causing the error message that you see. When fitting a binomial model, it is not necessary to specify an error term at level 1. This is because the level 1 error term is already included in the model, with a binomial distribution, when you specify a binomial response (It is attached to a specially created variable, which does not appear elsewhere in the model). When specifying models in the Equations window using the Graphical User Interface, you are not given the option to specify that any variable be random at level 1. Using commands or macros it is of course possible to issue a command that makes this specification, but this causes an error when MLwiN attempts to estimate the model. If you press the Start button after setting up a model like this using commands or a macro you will see the same error message. If you remove the command "setv 1 'cons' " from your macro the model should run as expected. For more information about binomial response models and level 1 residuals, see section C6.4 of the module on binary response models in our online training materials.

• I just tried to use MCMC methods in MLwiN but I always get error messages (wrong parameter...) even if I try to follow the tutorial in Chapter 10 of the MCMC manual.
  • This error may be caused by using a comma as the decimal separator. If you do not have the most recent version of MLwiN, you may find that upgrading to this version solves the problem. If you still experience the problem when using the most recent version, then try changing the decimal separator that your computer uses to a '.' (via Regional and Language Options in the Windows Control Panel).

• I'm trying to run a two-level multinomial model using MCMC: the outcome variable has 4 categories (cat 1 n=6168, cat 2 n=1160, cat 3 n=1608, cat 4 n=1393). The dataset comprises 200 areas and 10,329 individuals. When switching the estimation control from mql/pql to MCMC I get the following error message: "MCMC error 0315: prior variance matrix is not positive definitive" followed by "Error in MCMC start-up - estimation halted". I checked HELP in MLwiN and it indicated I needed to manually change a setting at column 1096 but insufficient information is provided as to how to do this. I subsequently sent an email to the multilevel listserv and received the following helpful response from Bill Browne…
  • "the MQL method must have produced a variance matrix at a higher level that is non positive definite i.e. it estimates a correlation between random effects outside the range -1 to 1. In C1096 the numbers should correspond to the ones you see in the equations window and are starting from the highest level the lower diagonal elements of all the variance matrices. My advice is to run in MQL/PQL then before switching to MCMC go into c1096 and switch off diagonal elements to 0 - to check you are doing this correctly if you have the equations window up next to the data window then when you change the value in the data window the corresponding value in the equations window will change. Once you have changed all the off-diagonal elements to zero switch to MCMC and things should run".
    • I followed Bill's advice and MCMC ran fine (which suggests I followed the advice correctly). However, I then added additional variables to my model and again went through the process of generating starting values using mql/pql and then switching to MCMC and the same two error messages returned, however, this time resetting the off-diagonal values to zero in c1096 did not fix the problem. And unfortunately my technical/programming knowledge of MCMC is very limited.
      • Bill's advice sounds spot on and I am surprised that it didn't solve the problem the second time round. Note, if you add any additional random effects then the rows of c1096 that you set to zero the second time will differ from the first time. Make sure that the second time you run the model the variance-covariance matrices look as Bill described before starting the MCMC chain. Also check whether any of the on-diagonal terms (i.e. the variances as opposed to covariances) are zero. If so, try changing them to 0.001.
        
        Note that not positive definite does NOT mean the matrix contains some elements which are negative. It is perfectly possible for a matrix which contains only positive elements to not be positive definite. Therefore when following the advice above it is important to change ALL the off-diagonal elements to 0, not just any negative off-diagonal elements.

• I am attempting to fit a 3-level proportional odds model with time (measured in months) as the first level, person (RID) as the second level, and institution (FID) as the third level.  In setting up an ordinal model I get the error message
  
  "Unexpanded level 2 id column (Month)must not contain consecutive repeated codes, in multivariate or multinomial models.  Use GENErate command to generate unique ID codes".
  
  I do not understand what is needed of the data and it isn't clear from the data manipulation menu how to use the GENE command.  Please advise me on this.
  • When you fit a multinomial model (whether ordinal or unordered), MLwiN needs your level 1 ID codes to obey the condition that the same value does not appear on adjacent rows of the dataset. So if your level 1 is Month, you can't for example have values of 1,2,3 for Individual 1 and 3,4,5 for Individual 2 because then the level 1 ID column will read '1,2,3,3,4,5,…' and that repeated 3 is a problem. (This does not apply to Normal response models, where repeated values like this are not a problem). To get around this, the simplest thing is to create a new variable to be your level 1 ID which has values 1,2,3,4,...,n where n is the length of your dataset: in other words a variable which is just a seqence from 1 to the length of the dataset, and which takes no account of any information about individuals or time points. This is what the error message is asking you to do when it tells you to use the GENErate command (more on this in a moment). You might think using a sequence like this as your level 1 ID is a problem because you are discarding all your information about when people were measured. However this information can still go into this model if you put Month in as an explanatory variable (you will probably want to do this anyway). The explanatory variable is the proper place for this information; all that is needed for the level 1 ID is that it should change from row to row, to signify that each row is a different occasion, it doesn't matter for the level 1 ID how far apart the occasions are or which people are measured on the same occasion.
    
    The reason that repeated values are a problem is that MLwiN needs to create an expanded dataset when you fit a multinomial model, as described in the User's Guide. (With a Normal response model, MLwiN does not expand the dataset). The process that it uses to expand the dataset requires that the level 1 IDs satisfy this condition. In the expanded dataset, a new level 1 is created and the level you specified as level 1 is now level 2, so the level 2 referred to in the error message is the level you specified as level 1.
    
    The sequence to use for level 1 in place of Months can be created either using a command or via the GUI. To create using the GUI, select 'Generate vector' from the 'Data Manipulation' menu. In the window that appears, select 'Sequence' under 'Type of vector'. Select any free column next to 'Output column' and type 1 next to 'Start number', the length of your dataset (this would be for example the length of your Month variable) next to 'End number' and 1 next to 'Step value' and click 'Generate'. To create using a command, in the Command interface window type 'Gene 1 n 1 c100', replacing n by the length of your dataset and c100 by any free column; for example if your Months variable is of length 4587 and column 48 is free you could type 'Gene 1 4587 1 c48'.

1. A value is clearly inconsistent with the model setup. This will often arise when you are running models which rely upon macros for implementation, such as MQL/PQL discrete response models. Check the settings carefully and in particular make sure that you have not overwritten any reserved columns or boxes.
2. The estimates are unexpected. In this case you may, of course, have a genuinely new result, but you should also make sure that you check every aspect of your model setup carefully. Try taking out parameters and reinserting them and look carefully at residuals and associated Normal plots etc.
3. Make sure that you have sorted the data within the worksheet to correspond to the multilevel structure you are modelling.
4. It is often a good idea to centre continuous (but not discrete) variables around their grand mean - this can avoid numerical problems.
5. Try building up your model in a different way. For example, start with a variance components model and add random coefficients rather than trying to fit many random coefficients from scratch.

• I have been using MLwiN to fit an ordered categorical model. In the first instance I have been doing this for a single level model and have been replicating the analysis in SPSS. When I fit a model including only the ordered response variable SPSS and MLwiN give the same answers more or less. When I add a categorical fixed effect explanatory variable, all but two of the standard errors of the parameter estimates are set to zero in MLWin. They are not in SPSS. Is there any explanation for this? I have suppressed the warning of negative variance in the iterative procedure to obtain convergence, is this the key? Is there any way round it? I am keen to pursue the use of MLWin because it is more powerful and I am particularly interested in the standard errors of the predictions. Thanks.
  • You can check whether these standard errors have really been set to zero or if they have been estimated but are very small. Check this by changing the display format for numbers from 3 decimal places to 3 significant figures. Go to: options Numbers (Display precision and missing value code) and change the selection from ‘decimal format’ to ‘signif digit format’; in the box ‘# significant digits’ select 3. If standard errors are still zero then you have some kind of estimation problem. One reason may well be: MLwiN is more sensitive than SPSS and Stata and can fail to estimate models that SPSS and Stata provide numbers for. This can be a good thing as MLwiN will fail when a model is poorly specified whilst SPSS/Stata will throw out results and you may not realise you have a problem. So make sure that your model makes sense and that all the variables in the model are sensible and have sensible distributions. You could try to see if the problem applies with other explanatory variables and an alternative ordered response. Other possibilities are: You have done something wrong in setting up the model in MLwiN. Check very carefully that the summary statistics for your variables look the same as in SPSS. Make sure that you have read the relevant chapter in the User Guide (chapters 9 and 11).Then try repeating your MLwiN/SPSS comparison for the simpler case of a binary response (i.e. collapse your ordered outcome down to two categories). As for ‘suppressing the warning of negative variance in the iteratice procedure’, there is no variance (apart from the implicit probit or logit variance) in single level ordered models so you should not be doing this.

• There is insufficient workspace - remedy - Increase worksheet size
• Too many windows programs open - remedy - Close some programs

1. Open the windows command line (Start Run)
2. Type the following in the windows command line:mlwin /sheetsize 5000. MLwiN will launch with its default worksheet size (5000k)
3. In MLwiN, open the worksheet window (Options worksheet)
4. Set the default worksheet size to a lower level which is appropriate for your computer and then click the use as defaults button. MLwiN will now be able to open on subsequent attempts to launch the software.

• I have just successfully installed MLwiN. However upon initiation of MLwiN, I now receive the message "Pre or Post file does not exist (post)".  Is this OK, or should it be repaired?
  • The pre- and postfiles should be located inside a directory called discrete in your MLwiN directory (in C:\Program Files). The first thing is to check whether they are actually there. The file names should be 'PRE' and 'POST'.
    
    If the files do not seem to be there, then try downloading and installing again. If you can see the files, then check that MLwiN is looking in the right place for them: from the Options menu select dIrectories and check that in the Fpath box it gives the path of the discrete folder (e.g. 'C:\Program Files\MLwiN v2.10\discrete') and in the Pre file box it says 'pre' and in the Post file box it says 'post'. If any of this has been mis-specified you can change it by selecting User defined settings above the boxes and then changing the text in the boxes as appropriate and clicking Done.
    
    If this problem has been encountered when running a macro that specifies a path for these files, check that the path is correctly specified in the macro.

• I'm taking the LEMMA Course and until yesterday everything was working perfectly, but today I just couldn't open the MLwiN Datafiles. Every time I try I get this message: "Run-time error '5': Invalid procedure call or argument". I've already install the latest version (2.10 beta 6), but it didn't work. I tried several times uninstalling and reinstalling the software, but it didn't work… Any ideas of what can I do? Many thanks in advance.
  • Has anything on your system changed between when you were able to open the worksheets and now? Examples might be other software being installed or removed. It might be worth manually clearing the MLwiN installation directory after removing it, before attempting to reinstall it. This is the directory where you chose to install it (usually C:\Program Files\MLwiN v2.10). If you have an account with administrative privileges on that machine it might also be worth checking to see if you have the same problems when running as that user.
    • As I don't have administrator rights in my computer, it is a pain each time I need to install a software. Finally I could open the files. As I realized I can open the old example files, what I did was to save the files in my computer and then change the extension from '.wsz' to '.ws' I know it is not the best, but it worked.

• When I click on the icon for 5.1.wsz in Module 5.1 I seem to get a notepad file that has a lot of blank characters, not a data file.
  • First note that the datasets for the LEMMA course will not open with MLwiN version 2.02: you will need version 2.10 or the teaching version (which you can download for free here). Make sure that you have one of these versions of MLwiN. If you do have the appropriate version but are experiencing this problem, then first try reinstalling your copy of MLwiN. If this fails, you can try downloading again and then reinstalling. If that doesn't work or if you cannot do this, there are two options: a work around or a fix.
    
    Option 1: Work around
    When you click on the link to the datafile, choose Save to computer instead of Open. Then start MLwiN and open the data file from MLwiN's File menu.
    
    Option 2: Fix
    The fix is to reassociate the data file's .wsz extension with MLwiN (so that Windows opens them in MLwiN if you double click them, or if you choose Open instead of Save to computer when downloading), which is pretty easy and takes just a minute.
    Again, when you click on the link to the datafile in your browser choose Save to computer rather than Open, and save for example to My Documents. Then open up My Documents or whichever folder you have saved the file into in Windows Explorer - so you can see the data file's icon. If the cause of the problem with opening the files is the situation this fix is designed for, then it should not have the MLwiN logo on it. (If the data file does have the MLwiN logo then there is probably a different cause of the problem and this fix will probably not work).
    The next part of these instructions is written correctly for Windows XP, but probably something similar will work for Windows Vista. Right click on the data file (i.e. click with the right mouse button, not the left one that people usually use), and choose the menu option Open With, then in the submenu select Choose Program. You should get a new window with a list of programs and a tick box labelled "Always use the selected program to open this kind of file" WHICH YOU SHOULD TICK, then select MLwiN, then click OK. If MLwiN is not in the list of programs, click the Browse button and locate and open the "mlwin.exe" file. It would normally be in the folder C:\Program Files\MLwiN v2\ or C:\Program Files\MLwiN v2.10. (Note that the icon for the program should be pale blue and white, not yellow and dark blue: the program with the yellow and dark blue icon is version 2.02 which will not open the LEMMA datafiles).
    After doing this, the data file on your computer should now have the MLwiN logo, and when you double click it should open up in MLwiN, and when you open files directly from your browser, they should open in MLwiN too.
    • I didn't reinstall, but I tried the work around (didn't work), and the fix (which did).

• I have worked through Module 5 up to p. 8 (P5.1.2) but when I try to produce the caterpillar plot (clicking 'apply' in the Plots tab), I get the error message: 'Failed to open Graphics Server', Clicking OK or closing produces the error message: 'The server is already running', Clicking or closing this message repeats the earlier message, and so on …
  • The following may fix this
    1) Save your worksheet
    2) Close all open copies of MLwiN
    3) Open task manager (right click the windows taskbar and click "Task Manager")
    4) Select the "Processes" tab
    5) Locate and select "gsw32.exe" from the list and click "End Process"
    6) Open MLwiN
    7) Load your saved worksheet
    8) Try producing the graph again

• When fitting discrete response models the data are transformed during the course of an iteration and later transformed back to their original values. If a problem occurs which interrupts an iteration the data may remain in their transformed state. If your data have been corrupted you must retrieve a correct worksheet. Corruption of data in this way will often become apparent when highly implausible results are seen
• An abnormal termination while running a generalised linear model or a macro may result in data corruption.
• You may have read data (at input or subsequently) into a protected or reserved column and since these columns are used by MLwiN to store various parameters anything in these columns will be overwritten.

• I fitted a model using version 2.02 and then upgraded to version 2.10
  Beta and fitted the model again. All the estimates of the coefficients and
  variance parameters were the same, but the -2*log(likelihood) value given
  was different.
  • We have found in some rare cases that MLwiN 2.10 Beta (subversions 1-9) produced incorrect likelihoods for models estimated with (R)IGLS. The problem does not apply to models estimated in MCMC (since there is no likelihood calculated for these models; the problem does not apply to the DIC). The problem was not present in previous release versions (2.02 and earlier). The problem was fixed in MLwiN Beta 2.10.
    
    Our research has found the problem to only occur in single level models with a large number of cases (>10,000). Furthermore, the problem does not occur if a second level is declared but no variance component is fitted at level 2.. If users have fitted a single level model in MLwiN 2.10 Beta (subversions 1-9), with only a single level hierarchy defined, the -2*log(likelihood) should be regarded as suspect and the model should be re-run in MLwiN 2.10. Further details…

• Running MCMC from a macro doesn't appear to work
• MLwiN gives different results to SAS and Stata
• I'm trying to export a number of variables from MLwiN, but only the first 5 appear in the text file
• I copied commands generated by MLwiN when I was using the GUI and pasted them into a macro, but when I ran the macro I got an error message
• I've recoded a categorical variable, but the list of category codes I see when I press Categories has not been updated
• Is the weights facility in MLwiN still experimental?
• Why is the log-likelihood value not displayed in the Equation Window when a Binomial or Poisson model has been fitted?
• My residuals column is too short
• My level 2 variables are being treated as level 1 variables

• I entered a categorical variable into my model as an explanatory variable, and although there are no observations in one of the categories of this variable, a dummy variable for this category was still included in the model. How can I remove it without removing all the dummy variables for this categorical variable?
  • When you enter a categorical variable as an explanatory variable (or as the response of a multinomial model), MLwiN will enter in all the categories of the explanatory variable even if some categories have no observations. The situation where some categories of a variable have no observations may occur if the variable had some categories with no observations in the original dataset you imported it from (perhaps a Stata or SPSS worksheet), or if you have recoded the variable so that some categories are combined (for example if you recode so that all observations in Category 3 are now in Category 2), or if you have deleted all records in that category of the variable from the dataset.
    
    An unneeded dummy explanatory variable can be removed from the model as described in the FAQ How can I constrain fixed parameters to zero?. Alternatively, before entering it into the model, you can update the category labels as described in the FAQ How do I update the category labels for a categorical variable? Now when you enter the variable into a model (whether as an explanatory variable or as the response of a multinomial model), only the new set of categories will be entered: any of the categories which had no observations will no longer be included. Note that if after following this procedure you recode the variable so that again some categories have no observations, or alter the data in any other way so that this happens, the categories with no observations will not automatically disappear: you will need to update the category labels again.
    
    A final possibility, if you know the code of the category which has no observations, is to use CATN to remove just the category/categories with no observations. How to do this is described in the FAQ How do I update the category labels for a categorical variable?; alternatively see p18 of the Command Manual. Since this removes the category from the variable, it will mean both that no dummy for that category is included when the categorical variable is entered as an explanatory variable and that the category will not be included when the categorical variable is used as the response of a multinomial model.

• How do I test if an interaction between a continuous and a categorical variable is significant?

• Is there an easier way to save and run a set of commands than copying into a text document and pasting one by one into the Command interface?
  • Yes, if you have a particular sequence of commands you want to run again, then perhaps the easiest thing is to put them in a macro. From the File menu, select New Macro. In the window that appears you can type your commands. Nothing will happen until you press the Execute button at the bottom. When you press the button, all the commands will be carried out. Most commands can be put into a macro in exactly the same way as you enter them in the Command interface window (there are a few exceptions). The macro can be saved at any time by selecting Save Macro or Save Macro as from the File menu (while the macro window is the active window). It is also possible to have open several macros at once.
    
    For more information on macros, see pp 82-84 of the Command Manual.

• Is there any way I can capture from the Equations window what I am setting up directly into a macro? The re-modelling in the Equations window is time consuming, and if I could obtain this in a macro, I could simply edit some of the macro commands.
  • Yes, you can. The easiest way to do this is to open the Command interface window (Data ManipulationCommand interface)  and deselect the User check box at the top. Now when you set up or make changes to your model in the Equations window the corresponding commands will appear in the Command interface window. Note that the corresponding commands will also appear when you use any other window: this does not only apply to the Equations window. Make sure you have the MLwiN command manual handy for interpreting the syntax: MLwiN will sometimes also issue some commands that you don’t need and this can cause problems (see here for an example of how to pick out the commands you want). The Command manual has not been updated recently however, so see also the Manual supplement for version 2.10 which documents commands for the new features in version 2.10 and also in section 8.4 includes some commands which work with version 2.02 as well as version 2.10 (note that not all the commands in this section work with version 2.02; if you are using version 2.02 you will need to experiment to see which work with this version). See also the MCMC manual, which includes some examples of writing and using macros which provide useful tips that apply in a more general context than just MCMC estimation.

• How can I specify a binomial response model using a macro?
• What is the command for specifying the denominator when fitting a binomial or multinomial model?
• Running MCMC from a macro doesn't appear to work
• Where are the time series macros?
• I can't get the LOGOn command to work
• I get an error message asking me to 'generate unique ID codes'. How do I do this?

• I have a logistic multilevel model (random intercept) and calculated the same model in Stata (xtmelogit), in SAS (proc glimmix) and in MLwiN. The fixed effects are quite similar but the random effects and the intercept differ. They are the same for SAS and Stata but not for MLwiN. In Stata and SAS I do get significant random variation in the intercept but in MLwiN I don't. How could that be? Do you have explanations??
  • SAS and Stata use maximum likelihood estimation for discrete response models while MLwiN uses quasi-likelihood methods (see p128 of the User's Guide for more details). The different estimation methods can produce slightly different results, and in the case where results lie close to the borderline for significance it is possible to find parameter values significantly different from 0 using one estimation method but not the other.
    
    It is known that quasi-likelihood methods give estimates for the random parameters which are biased downwards (see Rodríguez and Goldman, 2001). For this reason, we do not recommend that users take results from these estimation methods as final, but instead recommend that they should use MCMC estimation (after using quasi-likelihood estimation to get starting values). MCMC estimation gives unbiased parameter estimates; note however that the parameter chains and other diagnostics should be carefully checked so as to be sure that the burn in has been long enough for the chains to move away from what will probably be bad starting values, and that after burn in the chains have been run long enough to get accurate estimates. See MCMC estimation in MLwiN for more details of the diagnostics available and how to tell whether burn-ins and chains are long enough; and see our free online training materials (Section C 7.7* and the Technical Appendix to Module 7*) for more detailed discussion of estimation methods for binary response models.
    
    Reference: Rodríguez G. and Goldman N. (2001) Improved estimation procedures for multilevel models with binary response: a case-study. Journal of the Royal Statistical Society, Series A, 164, 339-355
    *You will need to log in to our training materials to view these web pages. Further details about the training materials

• How do I get rid of an unneeded dummy variable/ response category?
• I tried to run a binomial model and got an error message
• I tried to run a binomial model and got an error message (2)
• When I run MLwiN I get the error message "Pre or Post file does not exist (post)"
• When I get the error message "MCMC error 0315: prior variance matrix is not positive definitive" while running a multinomial model using MCMC, what exactly do I need to do to the numbers in C1096?

• I'm trying to set up a model using repeated measures data (with occasion within student within school). Looking at the example data, I see that level 1 ID has to be unique. Does this mean that the repeated measures have to be stored in the "wide" format?
  • No, MLwiN actually requires repeated measures data to be in the long, not the wide, format when it comes to analysis. The User's Guide (chapter 13, section 13.2) shows how to convert data from wide to long format. However this does not mean that the level 1 IDs are no longer unique. In repeated measures analysis, occasion (time) is regarded as level 1, student (in your case) becomes level 2, and so on. Nor does it matter that the natural level 1 ID, Occasion Number, will have the same value for more than one row in the dataset since we do not have to use this as our level 1 ID but can create a new ID variable. A unique level 1 ID, which will give a different number to each occasion-person combination, can be created by selecting Generate vector from the Data manipulation menu, and selecting Sequence under Type of vector, choosing a free Output column, typing 1 next to Start number, the length of your long dataset next to End number, and 1 next to Step value, and then clicking Generate. This can then be used as level 1 in the model, and a separate variable such as Time, Year or Occasion Number can be used as an explanatory variable.

• Is it possible to define an AR process (autocorrelation structure) for the level 1 random effects when we have repeated measures data?
  • Yes. For details of how to do this (with an example), see Section 5 on p72 of the MLwiN version 2.10 manual supplement. Note that although this is description appears in the MLwiN version 2.10 manual supplement, in fact the process is exactly the same if working in MLwiN version 2.02.

• I have a repeated measures dataset and would like to allow the level 1 error terms to be autocorrelated. I heard there were some macros which would do this, but cannot find them anywhere on your site.
  • The macros were removed when version 2.02 was released since they were found to be unstable. We now recommend an alternative method for setting up and running these models. This method is described in detail in Section 5 of the MLwiN 2.10 Beta Manual Supplement which is available from here. (Note that although this appears in the MLwiN 2.10 Beta Manual Supplement, exactly the same method can be used with MLwiN version 2.02). However, this method will only work with a Normal response model. Unfortunately we no longer provide the facility to estimate a binary response model with autocorrelated errors in MLwiN.

• I've run a model using MCMC, and when I looked at the trajectories for the parameters I realised that I had not set a long enough burn-in period. Can I change this retrospectively, or will I have to run the model again specifying the longer burn-in?
  • It is possible to get parameter estimates based on a longer burn-in after you have run a model. If you click on the trajectory graph for any parameter and answer Yes to the message Calculate MCMC diagnostics? then the MCMC diagnostics window will appear, and if you click on the Diagnostic Settings button at the bottom of this window you will see a box at the bottom of the window that appears, with Increase burn-in length by next to it. Type in here the iteration number up to which you want the burn-in period to run (this will give a burn-in length of the number you type in plus the burn-in length you were already using to run MCMC) and click Apply and Done. The 'posterior mean' estimate in the MCMC diagnostics window is now the parameter estimate under this longer burn-in and the 'SD' is the standard error of the parameter estimate. You can now click on the trajectory graph for any other parameter and the 'posterior mean' and the 'SD' will be adjusted to take into account the longer burn in (i.e. you do not need to click the Diagnostic Settings button for all the other parameters). Note however that the estimates displayed above the trajectory graphs in the Trajectories window will not be updated, and nor will the estimates displayed in the Equations window, the estimates stored in c1096-c1099, or the stacked parameter chains in c1090. Note also that the length of the monitoring chain (the iterations after the burn-in period) will be reduced by the same amount that the burn-in is increased.

• I get an error message 'wrong parameter...' when using MCMC
• When I get the error message "MCMC error 0315: prior variance matrix is not positive definitive" while running a multinomial model using MCMC, what exactly do I need to do to the numbers in C1096?

• When running a model in MLwiN, is it possible to constrain some of the parameters so they are forced to take on specified values instead of being freely estimated?
  • Yes, it is possible to specify constraints for both fixed and random parameters, and parameters can be constrained to be 0 or to be any specified number. In addition it is possible to specify more complicated constraints such as that two parameters should be equal or that the difference between the parameters should be a specified value.
    
    See the FAQs How can I constrain random parameters to zero?, How can I constrain fixed parameters to zero?, How can I constrain parameters to values other than zero? and How can I constrain two parameters to be equal? for details of how to constrain parameters

• Is there a way of constraining some of the covariances between the random effects to equal 0?
  • Yes, it is easy to constrain covariances between random effects to be zero. Simply click on the relevant covariance in the matrix in the Equations window, and in the window that appears asking whether you want to remove the covariance click Yes. The covariance will then be constrained to be zero as you will see since it will no longer appear as a coloured number with 3 decimal places but as a single digit 0 in black.
    
    It is also possible to do this using the command CLRE; for documentation of this see p35 of the Command Manual.
    
    See also How can I constrain parameters to values other than zero? and How can I constrain fixed parameters to zero?

1. the constraints remain stored in the column you have chosen (c11 in this case) and if you want to use them again you can click the load matrix from button and select c11 from the drop down box that appears, rather than enter them in the columns
2. more complicated constraints can also be specified this way: for example you can specify that two parameters should be equal (but not take on any specific value). See the FAQ How can I constrain two parameters to be equal? for how to do this.
3. this method can also be used to constrain parameters to zero, though there are quicker and easier ways to constrain parameters to zero via the Equations window (see FAQs How can I constrain random parameters to zero? and How can I constrain fixed parameters to zero?)

• Where can I find the random parameter matrix in MLwiN? How do I use this to work out the residual ('unexplained') variance at each level?
• What significance tests for both random and fixed parameters are available in MLwiN?
• How do I test whether two coefficients are equal?
• How do I test whether more than 2 coefficients are equal?
• How do I test if an interaction between a continuous and a categorical variable is significant?
• How can I calculate confidence intervals in MLwiN?

• I calculated the level 2 residuals for my model (with student as level 1 and tutorial group as level 2). I have 2124 individuals, and as expected I got 2124 residuals. But these residuals are all in the first 2124 rows of the worksheet. Since I have 3 students (level 1 units) per tutorial group (level 2 unit), the first 2124 rows should contain 2124/3 = 708 of the residuals, with the remaining residuals spread through the rest of the dataset. The rows after 2124 have no value in the residuals columns. How can I get the correct values of the residuals?
  • The output that you describe here is correct. MLwiN worksheets are not organised with one row corresponding to one record across the whole worksheet (see the FAQ Does each row correspond to a single record right across the MLwiN worksheet?). When you use the Residuals window to calculate the residuals at any level, the output MLwiN produces consists of just one entry in each output column for each unit at that level. The output is not arranged with missing values in all other rows corresponding to that unit in your original dataset, instead the values occupy consecutive places in their column with no gaps. So for example the residual in place 10 of c300 will be the residual for tutorial group 10, not the residual for tutorial group 4, even though row 10 of your original dataset corresponds to student 1 for tutorial group 4. The residuals will be in the same order as the tutorial groups in your original dataset, so in order to see which residual belongs to which tutorial group you will need to create a short column which contains the names/ codes of the tutorial groups, but only has one entry per tutorial group (so 2124 entries in all). To do this, from the Data manipulation menu select 'unreplicate'. The Take data window will appear. In the 'Take first entry in blocks defined by' drop down box, select the column which contains your tutorial groups, and also select this column under 'Input columns'. Under 'Output columns' select any free column. Click 'Add to action list' and 'Execute'. The column you chose under 'Output columns' will now have 2124 entries consisting of the code for each tutorial group in your dataset, and the rows of this column will correspond to the rows of your residuals columns, so you will be able to see which residual corresponds to which tutorial group.

• Where is the model fitting information stored in MLwiN?
• Should the comparative SD output when I calculate the residuals be different for each row?
• MLwiN is giving the standard errors of parameter estimates as 0, but I know from comparison with other software packages that the standard errors should not be 0

• I seem to remember that the facility to specify sampling
  weights (via the Weights option from the Model menu or the WEIGhts
  command) was introduced as an experimental feature. Is this still the
  case, or has thorough testing now been completed?
  • Yes, this feature is still experimental. We are currently checking that the weights facility works correctly for continuous response models. We will publish the results on our website when finished. Until then, users should continue to regard the weights facility as experimental. Users should also note that MLwiN does not offer the facility to use weights when using MCMC estimation: any weights specified will by ignored by MCMC. For this reason we do not recommend the use of weights in discrete response models (since we recommend MCMC estimation for these models), and will not be checking that the weights facility works correctly for discrete response models.

• I am hoping to use MLwiN to estimate a multiple membership model. However, I'm a little confused. My factor that is the multiple membership factor is "rater". So "rater" is analogous to secondary school in the example in the Mlwin manual. I'm trying to use the "WTCOl" command but it tells me that "categories in the ID column must run from 1..N with no gaps. Use MLREcode to create consecutive codes". However, this does not make sense for multiple membership models as there are several ID columns which would all need recoding together.
  • We strongly suggest that you estimate cross-classified and multiple membership models using MCMC estimation within MLwiN rather than IGLS. For full details see the MCMC manual. The manual details how the data needs to be set up and how to choose the weights etc

1. Create an indicator variable for each interval you want to fit a different polynomial to. In other words, if the cut points for your spline are 2, 7, 10, and expvar is your explanatory variable, and c20 onwards are all free columns then type in the Command interface:
   
   calc c20 = 'expvar' < 2
   calc c21 = ('expvar' >=2) & ('expvar' < 7)
   calc c22 = ('expvar' >= 7) & ('expvar' < 10)
   calc c23 = 'expvar' >= 10
   
   name c20 'int1'
   name c21 'int2'
   name c22 'int3'
   name c23 'int4'
   
   (Or you can use the Recode by range window with a new destination variable each time)
2. Create a new explanatory variable for each interval by multiplying 'expvar' by the indicator variable
   
   calc c24 = 'expvar' * 'int1'
   calc c25 = 'expvar' * 'int2'
   calc c26 = 'expvar' * 'int3'
   calc c27 = 'expvar' * 'int4'
   
   name c24 'expvar1'
   name c25 'expvar2'
   name c26 'expvar3'
   name c27 'expvar4'
3. Add each explanatory variable as a polynomial (first adding in the indicator variable for that interval to give each polynomial a different intercept)
   • Click Add Term at the bottom of the Equations window
   • Select int1 and click Done
   • Click Add Term again, select expvar1, tick the polynomial box and select the appropriate poly degree from the drop down box. Click Done
   • Repeat for the other 3 intervals
4. Set up constraints: the spline needs adjacent polynomials to have the same value and the same derivatives (up to the (n-1)th, where n is the degree of the polynomials) at the point where they meet. If there are random effects on any of the terms in the spline, we also need to make sure that the variance at each level is the same for adjacent polynomials at the point where they meet. For details of how to specify constraints on the parameters see the FCON and RCON commands in the Command manual, or in the Help see Introduction to MLwiN MLwiN Interface Menu items Model Menu Constrained parameters.
   
   For example, if we have a cubic for each polynomial and have added the terms in the order described above so that the Equations window shows
   
   response = int1_ij + expvar1^1_ij + expvar1^2_ij + expvar1^3_ij + int2_ij + expvar2^1_ij + expvar2^2_ij + expvar2^3_ij +…+ e_ij cons,
   
   and we have a level 2 random effect on each intercept and linear term ( int1_ij, expvar1^1_ij, int2_ij   expvar2^1_ij,…),  then to deal with the first join, between interval 1 and interval 2, we need 4 constraints:
   
   These polynomials meet at expvar1 = expvar2 = 2. The first constraint is that the value of the polynomials should be the same at this point, so we need
    +  × 2 +  × 2² +  × 2³  =  +  × 2 +  × 2² +  × 2³
   Our constraint will be  + 2  + 4 + 8 -  - 2 - 4 - 8 = 0.
   The second constraint is that the first derivatives of these polynomials are equal at this point, so we need
    + 2 × 2 + 3 × 2²  =  + 2 × 2 + 3 × 2²
   so our constraint will be   + 4 + 12 -  - 4 - 12 = 0
   Similarly our third constraint, that the second derivatives of these polynomials are equal at 2, will be 2 + 12  - 2 - 12 = 0.
   Our fourth constraint is that the level 2 variance due to the random effects on the first polynomial and the level 2 variance due to the random effects on the second polynomial should be equal at expvar = 2. In other words,
    × 1 +  × 1 × 2 +  × 2² =  × 1 +  × 1 × 2 +  × 2²
   Our constraint will be  + 2 + 4 -  - 2- 4 = 0.
   
   We will have two further similar sets of four constraints to make sure the value, derivatives and level 2 variance are equal at the other cut points.

• I have some level 2 variables (i.e. variables which have the same value for all individuals in the same level 2 unit) which I put in my model as explanatory variables. The Equations window shows some of these with an ij subscript, not a j subscript, indicating that MLwiN thinks these are level 1 variables. How do I tell MLwiN they are level 2 variables?
  • MLwiN works out automatically whether a variable is a level 2 variable. It does this by checking whether there is any level 2 unit where not all individuals have the same value of the variable. If there is (at least 1) level 2 unit like this, then it concludes that the variable is a level 1 variable. If there are no level 2 units like this, so that in all level 2 units all individuals have the same value of the variable, then it concludes that the variable is a level 2 variable.
    
    If MLwiN gives one of your level 2 variables an ij subscript in the Equations window, showing that it thinks this variable is a level 1 variable, then you should check for mistakes in your data: a level 2 unit where not all individuals have the same value of the variable. You can do this by inspecting your data, of course, but a quicker and less error-prone method is as follows (to check a level 2 variable called popden):
    
    From the Data Manipulations menu, select Multilevel data manipulations. In the window that appears, under Operation select Minimum and under On blocks defined by select the column which contains your level 2 identifiers. Under Input columns select popden and under Output columns select any free column (say c70). Click Add to action list and Execute. Now from under Operation select Maximum and select another free column (say c71), leave everything else the same and click Add to action list and Execute again. Now c70 contains the smallest value of popden for each level 2 unit and c71 contains the largest value of popden for each level 2 unit. If popden is supposed to be a level 2 variable and if there are no mistakes in the data then c70 should be identical to c71. We check this by typing in the Command interface window (available from the Data Manipulation menu) 'calc c72=c71-c70' -that is we are calculating the difference between c70 and c71 which we expect to be 0 for every row. We can now check whether the data are correctly entered by looking in the Names window. If c72 is 0 for every row then in Names window in the row for c72 we will see 0 under min and 0 under max. If we do not this tells us that in at least one case, c70 and c71 were not identical, so the minimum and maximum values of popden were not equal for each level 2 unit- i.e. for some level 2 unit different level 1 units had different values of popden. In order to find out which level 2 unit (and whether this is the case for more than one level 2 unit), we generate a column that will keep track of which row things are on. We do this by selecting Generate vector from the Data Manipulation menu, selecting Sequence under Type of vector, selecting a free column (e.g. c73) next to Output column, typing 1 next to Start number, the length of the dataset next to End number, and 1 next to Step value, and clicking Generate. Now from the Data Manipulation menu select Select or omit cases, under Condition to select or omit on type c72 != 0, under Input columns select c72 and c73 and under Output columns select two free columns (e.g. c74 and c75), and click Add to action list and Execute. We have now created two new columns which have kept only information from rows where c72 was not 0; c74 contains the value of c72 for those rows and c75 contains the value of c73 for those rows (and will tell us which row of the original dataset the values came from). If we look at c74 and c75 in the Data window we can see the nonzero values of c72 and which row of the original dataset each comes from. Now if we look at these rows in our original dataset (looking at the column with the level 2 IDs and popden) we should be able to see the discrepancy, and edit the data appropriately.
    
    Note that in some cases we may find that we got a nonzero value simply because the value of popden was missing (then the corresponding value in c74 will be MISSING). If the value of popden is missing for all individuals in a level 2 unit, then we will find entries for these individuals in c74 and c75, but this will not stop MLwiN treating popden as a level 2 variable. If, on the other hand, the value of popden is missing for only some individuals in a level 2 unit, then MLwiN will treat popden as a level 1 variable.