"convergence not achieved" in multilevel logit model

[Gayoung Choi]

Hello,

I have been working on running a random slope model, on longitudinal data (in long form) using the logit model. However, I have encountered an issue that I cannot resolve, so I wanted to reach out to you for guidance.

Here is the description of the model:

• Focal variable (outcome): Work Assessment (binary, n=1 for 682 cases, 0 for 8,701 cases)
• Main predictor: Early Retirement Pressure (binary)
• Total number of observations in the dataset: 57,976
• Number of observations when running this model: 3,463 with 1,363 individuals

My question is as follows: I attempted to implement the random slope model as you taught us last time. The random intercept code works well, but when I include the random slope for centered age, I encounter a "convergence" issue, and the maximum log-likelihood is reported as "not concave."

(Random Intercept) melogit workassess i.female edu lg_hinc i.urban $health i.earlyret##c.c_age || pid:, cov(un)

(Random Slope Model) melogit workassess i.female edu lg_hinc i.urban $health i.earlyret##c.c_age || pid: c_age, cov(un)

Is there any way to modify the model settings in this case?

And Here is my result.

Iteration 297: log likelihood = -921.96692 (not concave)
Iteration 298: log likelihood = -921.96692 (not concave)
Iteration 299: log likelihood = -921.96692 (not concave)
Iteration 300: log likelihood = -921.96692 (not concave)
convergence not achieved

Mixed-effects logistic regression Number of obs = 3,463
Group variable: pid Number of groups = 1,363

Obs per group:
min = 1
avg = 2.5
max = 4

Integration method: mvaghermite Integration pts. = 7

Wald chi2(8) = 80.77
Log likelihood = -921.96692 Prob > chi2 = 0.0000
----------------------------------------------------------------------------------
workassess | Coefficient Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
c_age | -.0023769 .017445 -0.14 0.892 -.0365685 .0318147
1.female | .4622551 .1717717 2.69 0.007 .1255889 .7989214
edu | -.2801203 .138019 -2.03 0.042 -.5506326 -.0096081
lg_hinc | -.3565346 .1255152 -2.84 0.005 -.6025399 -.1105292
1.urban | .2396985 .2315582 1.04 0.301 -.2141473 .6935443
1.firselfhealth | .8681222 .1615322 5.37 0.000 .5515249 1.184719
chronic | .195936 .0959162 2.04 0.041 .0079438 .3839283
1.earlyret | .463443 .1886819 2.46 0.014 .0936333 .8332527
_cons | -.7321033 1.005356 -0.73 0.466 -2.702565 1.238358
-----------------+----------------------------------------------------------------
pid |
var(c_age)| .0051863 3.91e-07 .0051855 .005187
var(_cons)| .9579369 .0000659 .9578077 .9580661
-----------------+----------------------------------------------------------------
pid |
cov(c_age,_cons)| .070485 . . . . .
----------------------------------------------------------------------------------
convergence not achieved





Additionally, I have come across the use of the "gsem" command for multilevel models. Since "gsem" is a structural equation modeling command, would it be appropriate to use it as an alternative to the current code?

Thank you for your assistance.

[Maarten Buis]

For multilevel models it often helps to center all continuous variables, in your case also edu and lg_hinc (assuming that lg_hinc is the logarithm of household income, then you first take the logarithm and than center not the other way around). My intuition of why this is is that a multilevel model includes a model for your constant. If that constant is near the limit or outside the range of the data, then multilevel models sometimes have trouble with that. Centering makes sure that the constant is well within the range of the data, making it easier for the model.