multilevel modeling using panel data - matrix must be positi

[morning03]

Hi. I am a new user of runmlwin. I am estimating a multilevel logistic model on the propensity of a residential move using panel data with random intercept. I am using the wave as level 1 unit and the household is as the level 2 unit... First I estimated the model using igls and the results seem fine. However, when I try to fit an mcmc model using the results from the first model as initial values, I keep on getting the "matrix must be positive definite.." error. I am not sure what is causing it.... Any help will be much appreciated.

Have a pleasant week ahead.

Thanks,
Arturo

[GeorgeLeckie]

Hi Arturo,

You typically get this message when you have fitted a model with random coefficients and the resulting random part covariance matrix is badly behaved, typically the correlation between the random intercept and one of the random coefficient effects lies outside the -1 to +1 range. This can happen when the model is too complex for the data, or if the model is nonsensical in some way. If you continue to get this error, please paste your sytnax and output into your reply so that we can better see what the cause of the error message might be.

Best wishes

George

[morning03]

Thank you very much for the quick response, George, it's much appreciated.

Actually, before I estimated a 2-level model, I tried estimating a 3-level model since I am using individual-level panel data (i.e., wave-level1, individual id-level2, family id-level3). However, the variance for the random individual-level intercept is zero so I just proceeded to estimating a 2-level model (i.e., wave-level1, family id-level2). While the IGLS estimation worked, the MCMC estimation encountered an error that the matrix must be positive definite. I'm thinking if specifying 0 for all variance/covariance parameters will do the trick.

Anyhow, here are the codes that I'm using and the corresponding outputs from Stata and MlWin2.25:


Thank you very much for your time.

Have a nice day ahead,
Arturo

Code: Select all

sort family_id wave
runmlwin Y cons i.X1 X2 X3 X4 X5 X6 X7 X8 i.X9 X10 X11 X12 X13 i.X14 X15 X16 i.X17///
if responding_person == 1 & Xsingle == 1 & units_included_foranalysis == 1, level2(family_id: cons)  level1(wave:) discrete(distribution(binomial) link(logit) denominator(cons)) ///
nopause mlwinpath(C:\Program Files\MLwiN v2.25\mlwin.exe)




      MLwiN 2.25 multilevel model                     Number of obs      =     29344
      Binomial logit response model
      Estimation algorithm: IGLS, MQL1
      
      --------------------------------------------------------------------------
                              |   No. of       Observations per Group
       Level Variable  |   Groups    Minimum    Average    Maximum
      ----------------+--------------------------------------------------------
         family_id       |     6756          1              4.3         35
      --------------------------------------------------------------------------
      
      Run time (seconds)   =      21.75
      Number of iterations =          8
      ----------------------------------------------------------------------------------------------
             Y             |      Coef.      Std. Err.      z        P>|z|     [95% Conf. Interval]
      -----------------+---------------------------------------------------------------------------
              cons       |  -1.605837   .0888317   -18.08   0.000    -1.779943    -1.43173
          _1b_X1       |          0          0        .      .             0           0
            _2_X1       |   1.054539    .042879    24.59   0.000     .9704979     1.13858
            _3_X1       |  -1.298693    .957877    -1.36   0.175    -3.176098    .5787112
            _4_X1       |   1.125275   .0856164    13.14   0.000     .9574701     1.29308
                 X2       |  -.1114131   .0072013   -15.47   0.000    -.1255275   -.0972987
                 X3       |  -.0351183   .0015105   -23.25   0.000    -.0380789   -.0321577
                 X4       |    .000166   .0000862     1.92   0.054    -3.06e-06     .000335
                 X5       |  -.0853965   .0367195    -2.33   0.020    -.1573654   -.0134275
                 X6       |   .1715977   .0700068     2.45   0.014     .0343869    .3088086
                 X7       |  -.0915078    .065917    -1.39   0.165    -.2207027    .0376871
                 X8       |   1.467441   .0504637    29.08   0.000     1.368534    1.566348
          _1b_X9       |          0          0        .      .             0           0
            _2_X9       |  -.0726749   .1493732    -0.49   0.627    -.3654411    .2200913
            _3_X9       |  -.2001464    .146699    -1.36   0.172    -.4876711    .0873783
                 X10     |  -.0409512   .1493137    -0.27   0.784    -.3336007    .2516984
                 X11     |   -.284316   .1538169    -1.85   0.065    -.5857916    .0171596
                 X12     |  -.2165901     .16999    -1.27   0.203    -.5497642    .1165841
                 X13     |   .0690696   .0455874     1.52   0.130    -.0202802    .1584193
          _1b_X14     |          0          0        .      .             0           0
            _2_X14     |   .2012782    .071133     2.83   0.005     .0618601    .3406964
            _3_X14     |   .4663865   .0731933     6.37   0.000     .3229302    .6098428
            _4_X14     |   .0057812   .0486005     0.12   0.905    -.0894741    .1010365
                 X15     |   4.32e-07   4.83e-07     0.89   0.371    -5.14e-07    1.38e-06
                 X16     |   .0295688   .0172871     1.71   0.087    -.0043132    .0634508
          _1b_X17    |          0          0        .      .             0           0
            _2_X17    |  -.0532726   .0490182    -1.09   0.277    -.1493464    .0428012
            _3_X17    |   .1925178   .0492156     3.91   0.000     .0960569    .2889786
            _4_X17    |  -.1624762   .0663194    -2.45   0.014    -.2924598   -.0324926
            _5_X17    |   .0095187   .0659811     0.14   0.885    -.1198019    .1388393
            _6_X17    |   .1133617   .1024594     1.11   0.269     -.087455    .3141784
            _7_X17    |   .5418286   .1759747     3.08   0.002     .1969245    .8867327
            _8_X17    |   .0212009   .1354922     0.16   0.876    -.2443589    .2867608
      ----------------------------------------------------------------------------------------------
      
      ---------------------------------------------------------------------------------------------
         Random-effects Parameters |   Estimate   Std. Err.     [95% Conf. Interval]
      -----------------------------+---------------------------------------------------------------
      Level 2: family_id             |
                         var(cons)            |   .4072275   .0308308      .3468003    .4676547
      --------------------------------------------------------------------------------------------


sort family_id wave
runmlwin Y cons i.X1 X2 X3 X4 X5 X6 X7 X8 i.X9 X10 X11 X12 X13 i.X14 X15 X16 i.X17///
if responding_person == 1 & Xsingle == 1 & units_included_foranalysis == 1, level2(family_id: cons)  level1(wave:) mcmc(on) initsprevious discrete(distribution(binomial) link(logit) denominator(cons)) ///
nopause mlwinpath(C:\Program Files\MLwiN v2.25\mlwin.exe)

MLWin Error:

"error while obeying batch file
C:\data\Local\Temp\ST_1o000008.tmp at line number 1326: WSET

MCMC Error 0003: Matrix must be positive definite for inversion."

[GeorgeLeckie]

Hi Arturo,

Look at your fixed part parameter estimates. Some of them are exactly zero (looks like perfect multicollinearity). I suspect that this is the source of your problem. These parameters are not identified.

I suspect if you correct your model specification so that you no longer have these model specification errors you will no longer see the error message that arises when you switch to MCMC.

The error message says

"Matrix must be positive definite for inversion"

in your example, I believe this is referring to the sampling covariance matrix (initially I had presumed the problem lay with parameter estimates covariance matrix, but this is not the case as your model does not have any random coefficients and so you only have one random part parameter at each level and so no matrices).

The sampling covariance matrix [e(V) in Stata parlance] is used in the adapting phase of the Metropolis Hastings MCMC algorithm which is used to fit discrete response models such as yours in MLwiN.

Best wishes

George

[morning03]

Thanks a lot, George.

You're right, the 0's should not be there. However, the 0's correspond to the base categories of the categorical variables X1, X9, X14 and X17. I was able to proceed to MCMC estimation after creating dummy variables for these four variables (and excluding the base categories in the model specification) instead of using "i.X" in my stata code.

Many thanks again.

Have a nice week ahead,
Arturo

[GeorgeLeckie]

Great, I'm glad runmlwin now works for you
Best wishes
George