Chi-Square Test for MCAR in LCA PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
Message/Author
 Dipali Rinker posted on Friday, December 06, 2013 - 12:06 pm
Hello,

I am running an LCA, and was wondering what a significant Pearson Chi-square test for MCAR means.

Thank you,
Dipali
 Tihomir Asparouhov posted on Friday, December 06, 2013 - 3:22 pm
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.
 Tihomir Asparouhov posted on Friday, December 06, 2013 - 5:02 pm
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.
 Dipali Rinker posted on Saturday, December 07, 2013 - 1:19 pm
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 Chi-Square test for the MCAR under the Unrestricted Latent Class Indicator Model is significant, while the Likelihood Ratio Chi-Square test for MCAR under the Unrestricted Latent Class Indicator Model is non-significant. How do I interpret this and should I worry about this?

Thank you!
 Bengt O. Muthen posted on Wednesday, December 12, 2018 - 5:10 pm
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 Chi-Square tests or my model?
 Bengt O. Muthen posted on Thursday, December 13, 2018 - 6:57 am
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.
 Bengt O. Muthen posted on Friday, December 14, 2018 - 11:49 am
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.
 Bengt O. Muthen posted on Friday, December 14, 2018 - 1:04 pm
I can't say anything more without you sending the output to Support.
 Wossenseged Jemberie posted on Tuesday, March 05, 2019 - 2:57 am
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 Chi-sq. 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:
******
Chi-Square Test for MCAR under the Unrestricted Latent Class Indicator Model

Pearson Chi-Square

Value 2940.469
Degrees of Freedom 21984
P-Value 1.0000

Likelihood Ratio Chi-Square

Value 1543.414
Degrees of Freedom 21984
P-Value 1.0000
 Bengt O. Muthen posted on Tuesday, March 05, 2019 - 2:00 pm
When chi-square 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 chi-square are therefore not fulfilled.
 Tihomir Asparouhov posted on Tuesday, March 05, 2019 - 5:35 pm
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 chi-squares 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).
 Wossenseged Jemberie posted on Wednesday, March 06, 2019 - 2:59 am
thank you very much for your answers.
 rgm smeets posted on Monday, March 11, 2019 - 8:22 am
My Chi-square 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 Chi-square test take into account the missing values in all types of variables (so categorical, nominal as well as continuous)?
 Tihomir Asparouhov posted on Wednesday, March 13, 2019 - 9:00 am
It applies only to the categorical variables. The reference for the test is

https://www.tandfonline.com/doi/abs/10.1080/01621459.1982.10477795
Back to top
Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action: