

Growth curve model with binary outcome 

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Dear all, I am using a growth curve model in order to analyze change (i.e., treatment effect) in a binary indicator across 2 measurement occasions (Voelkle, 2007, Psychology Science, 49, 375–414). Unfortunately, the model does not provide standard errors / pvalues and MPlus says “The degrees of freedom for this model are negative. The model is not identified.” I tried different options for estimator, weight, cluster, bootstrap etc. – nothing worked. Is something wrong with the model or is it underestimated due to the fact that I only have 2 time points? I’m wondering about this because a model with a continuous indicator (also two time points) can easily be estimated. In addition, when I add a third time point (+ 1 random binary variable) the model does not work either, but when I have four time points (+ 2 random binary variables) it suddenly worked fine. Thanks in advance for your answers! The code with 2 time Points is: MODEL: i s  out0@0 out1@1 ; out0@0 out1@0 ; i s ON group ; s ON i ; 


With 2 time points and continuous outcomes you have for each group 5 pieces of information: 2 means, 2 var's, and 1 cov. With binary outcomes you have only 3 pieces. With 2 time points and binary outcomes your model has more parameters than that. Note that you don't want to fix the residual variances at zero. Note also that you cannot identify the variance of s with only 2 time points for either the continuous or binary case. 


Dear Prof. Muthen, Thank you very much for the information. we are not quite sure about your explanations; as far as we understand it, the model with a continuous manifest outcome is fully saturated for two points in time if the residuals of the measurement model are fixed at zero (this is just another notation of a random anova). Please see a piece of output below. Unfortunately, we are not able to adopt this notation if the manifest variables are binary. Moreover, we don`t understand why we only have 3 pieces of information in this case. Thanks again for further explanations in advance. Output for continuous model: i s kost0@0 kost1@1; kost0@0 kost1@0; Estimate I  KOST0 1.000 KOST1 1.000 S  KOST0 0.000 KOST1 1.000 S WITH I 2359.906 Means I 33.122 S 5.482 Intercepts KOST0 0.000 KOST1 0.000 Variances I 4330.523 S 6831.682 Residual Variances KOST0 0.000 KOST1 0.000 


The sample statistics for binary variables are thresholds and correlations. Variances are not model parameters for binary variables. For two binary variables, you have two thresholds and one correlation, These are the three pieces of information. 

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