Getting different standard errors using mplus and lmer in R

Question

I am fitting the same mixed effects model using mplus and lmer in R. Since mplus uses full information maximum likelihood (FIML) method, I selected REML=FALSE in the lmer package.

I am getting same point estimates from two models. However the standard errors are different.

The results using lmer pacakge

glm_mo=lmer(DEP ~ gender + (1| cluster), data=data_cmd_long, REML = FALSE)

The results using mplus

    MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Within Level

 DEP        ON
    GENDER             0.088      0.015      5.973      0.000

 Residual Variances
    DEP                0.072      0.004     17.988      0.000

Between Level

 Means
    DEP                0.689      0.020     34.606      0.000

 Variances
    DEP                0.001      0.001      1.531      0.126

What may be the reason that causing different standard errors?

I thought by defining REML=FALSE make results equivalent using two approaches.

Any help will be highly appreciated.

Thank you.

Edit:

This my input code for mplus

Variable:
    names =  aid dep gender cluster ;
    usevariables = dep gender cluster ;
   within= gender; 
MISSING IS cluster (9999) dep (9999);

CLUSTER = cluster;
 

  Analysis: TYPE = TWOLEVEL random ;
  estimator = mlr;
 

Model:
        %WITHIN%
      dep on gender  ;
      %BETWEEN%
        dep;

Some other related portion of the output from mplus

Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                   100
Convergence criterion                                    0.100D-05
Maximum number of EM iterations                                500
Convergence criteria for the EM algorithm
  Loglikelihood change                                   0.100D-02
  Relative loglikelihood change                          0.100D-05
  Derivative                                             0.100D-03
Minimum variance                                         0.100D-03
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Optimization algorithm                                         EMA

Results based on ML option in mplus

MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Within Level

 DEP        ON
    GENDER             0.088      0.014      6.083      0.000

 Residual Variances
    DEP                0.072      0.003     25.654      0.000

Between Level

 Means
    DEP                0.689      0.022     30.934      0.000

 Variances
    DEP                0.001      0.001      1.515      0.130

Answer 1

It's important that you are fitting exactly the same models, in order to obtain similar output. Things to check are:

• use the same estimation method, eg maximum likelihood without robust standard errors

• use the same optimiser. This is usually more of a issue with GLMMs.

• use the same starting values. Again this is more relevant to GLMMs, but can sometimes also be an issue for LMMs

• where you have missing data, a good starting point is to use listwise deletion before running each model. Once you have similar output, you can then decide on the proper way to handle missingness.