Message/Author 


Hello, I am running an LCA, and was wondering what a significant Pearson Chisquare test for MCAR means. Thank you, Dipali 


It means that the MCAR hypothesis is rejected, i.e., the missing data are not missing completely at random and most likely the probability of missingness depends on other variables in the model (i.e. it is not constant across all observations). More information on that particular test is available in Fuchs (1982) Maximum Likelihood Estimation and Model Selection in Contingency Tables With Missing Data J of Amer Stat Assn. 


Also, I forgot to say, you don't need to worry about this. The estimates of the LCA model are still unbiased even though MCAR doesn't hold. That is because the ML estimation yields unbiased estimates under the more general MAR hypothesis. 


Hello, thank you for your response. Yes, I was wondering in what way this would affect my estimates. Thank you again, Best, Dipali 

rgm smeets posted on Wednesday, December 12, 2018  4:58 am



Dear, I also ran a LCA and the Pearson ChiSquare test for the MCAR under the Unrestricted Latent Class Indicator Model is significant, while the Likelihood Ratio ChiSquare test for MCAR under the Unrestricted Latent Class Indicator Model is nonsignificant. How do I interpret this and should I worry about this? Thank you! 


My rule of thumb is  if they disagree, don't use them because their assumptions (like large enough expected cell sizes) are not fulfilled well enough. 

rgm smeets posted on Thursday, December 13, 2018  2:22 am



Dear Bengt, I am not sure about what you mean with "don't use them". Do you mean the ChiSquare tests or my model? 


Don't use the tests  don't rely on them in that case. 

rgm smeets posted on Friday, December 14, 2018  4:31 am



Thank you mister Muthen. I have another question about my probability scale results. In two categories of one variable in one class, the Standard Error is above 1. How should I interpret this? Is this just something to report? 

rgm smeets posted on Friday, December 14, 2018  5:09 am



additional to my last question (sorry for this), the two categories that have a Standard Error above 1 in the probability results, belong to the item that is said to be set at extreme values in the optimization. Maybe this has influenced the SE. 


We need to see what you are looking at  send your output with these questions to Support along with your license number. 

rgm smeets posted on Friday, December 14, 2018  12:07 pm



Dear mister Muthen, Unfortunately I cannot send any output as I am working in a protected environment. It seems like my model is working well (no convergence problems en Logl is replicated), I only received the warning that some or more logit thresholds were approached and set at extreme value and now I see that the SE in the probability results for two categories within one item is above 1. I hope you can stil help me. 


I can't say anything more without you sending the output to Support. 


Dear Drs. Bengt and Linda Muthen, I just bought Mplus and am conducting LCA (I am very new to Mplus, so apologies if my questions are elemntary. I am catching up with lecture notes and videos). My question is that the pvalue for Chisq. test for MCAR (both Pearson and LR) show me 1.0000. Does it mean that I can say with confidence missingess is at completely random and I dont need to handle missingness? Thank you! The output is below: ****** ChiSquare Test for MCAR under the Unrestricted Latent Class Indicator Model Pearson ChiSquare Value 2940.469 Degrees of Freedom 21984 PValue 1.0000 Likelihood Ratio ChiSquare Value 1543.414 Degrees of Freedom 21984 PValue 1.0000 


When chisquare values from Pearson and Likelihood ratio are this different, you are probably best off not trusting either. The high degrees of freedom suggests that you have many cells in your frequency table so that you are likely to have low numbers or zero in many cells and the assumptions behind chisquare are therefore not fulfilled. 


Also note that establishing MCAR missingness is somewhat symbolic. The ML estimator is guaranteed to work well for both MCAR and MAR. It appears that there is no strong MAR missingness and possibly one can claim MCAR (with a footnote about chisquares with huge DF) you can't really gain much from it. You should treat the missing data the way you have done, i.e., using FIML (i.e. ML estimator). It would not be recommended to use listwise deletion. Even tough (under MCAR) it is a valid approach you would still be loosing information if you use listwise deletion (larger SE). 


thank you very much for your answers. 

rgm smeets posted on Monday, March 11, 2019  8:22 am



My Chisquare test for MCAR under the Unrestricted Latent Class Indicator Model is not significant (implying that the missing data are MCAR). I have categorical, nominal and continuous data in my dataset. Does this Chisquare test take into account the missing values in all types of variables (so categorical, nominal as well as continuous)? 


It applies only to the categorical variables. The reference for the test is https://www.tandfonline.com/doi/abs/10.1080/01621459.1982.10477795 

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