Empty Bivariate Table is not equal to 1? PreviousNext
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 Ian Zajac posted on Wednesday, August 15, 2007 - 8:03 pm
In am performing a CFA with dichotomous outcome variables. I get the EMPTY CELL warning regarding the bivariate table and the relevant variable names.

This, I have read, means that the tetrachoric correlation for a pair of variables is equal to 1. However, when I inspect the sample tetrachoric matrix, this is not the case at all. The correlations are generally moderate (@ .45 or so).

Am I looking at the right correlations?
Also, could this be due to highly skewed variables? It appears that all the suspect variables are (i.e., >95% correct/incorrect).

Regards -
ian.
 Linda K. Muthen posted on Thursday, August 16, 2007 - 6:45 am
Empty cells in bivariate tables are most common when variables have extreme cuts like 95/5. Empty cells imply correlations of one. I'm not sure what you are looking at so can't say if you are looking at the right thing. If you want further clarifiction, please send your input, data, output, and license number to support@statmodel.com.
 Ian Zajac posted on Monday, August 20, 2007 - 6:14 pm
Hi Linda,

OUPUT is sampstat

You get a number of statistics including
> SUMMARY OF CATEGORICAL DATA PROPORTIONS
> SAMPLE STATISTICS
> ESTIMATED SAMPLE STATISTICS
> SAMPLE TETRACHORIC CORRELATIONS

Given the warnings, I would expect than when I inspect the 'Sample tetrachoric correlations', I would find a correlation of 1 between the variables noted in the warnings. But, this isn't the case. The correlations are actually moderate and are never equal to 1.

Should I be using a different output command?

Regards -
Ian.
 Linda K. Muthen posted on Thursday, August 23, 2007 - 11:14 am
I would need to see exactly what you are getting to answer you. Please send your input, data, output, and license number to support@statmodel.com.
 Theresa Dicke posted on Wednesday, March 30, 2011 - 2:58 am
Dear Linda,
I have the exact same problem as Ian:"I get the EMPTY CELL warning regarding the bivariate table and the relevant variable names.

This, I have read, means that the tetrachoric correlation for a pair of variables is equal to 1. However, when I inspect the sample tetrachoric matrix, this is not the case at all. The correlations are generally moderate (@ .45 or so). "

Is there a solution to this problem?

many thanks in advance!
kind regards, Theresa
 Linda K. Muthen posted on Wednesday, March 30, 2011 - 6:52 am
The sample correlation matrix will not necessarily show one. That is the problem. For binary variables , you need bivariate tables without zero cells for this type of analysis.
 Helen Skerman posted on Wednesday, June 22, 2011 - 3:51 pm
For ordinal variables, is it necessary to ensure there are no empty cells in any of the bivariate tables. I am investigating the structure in 32 variables with 4 categories and will exclude 6 of the low frequency variables to address this problem. However, is it OK if there is the occasional empty cell remaining?

Many thanks.
 Linda K. Muthen posted on Thursday, June 23, 2011 - 11:08 am
It should be okay to have some zero cells for ordinal variables. The problem is that there is no way to tell if it is okay. I would be cautious.
 Rebecca Fortgang posted on Monday, June 11, 2012 - 1:17 pm
I am having just the same problem that Ian and Theresa have had. I get a slew of warning messages telling me that the bivariate table of (dichotomous variable) and (other dichotomous variable) has an empty cell. What does this mean? If I calculate the bivariate correlation between those two variables, it is not 1, and it is also not 0. It is generally moderate, just as Ian described.
 Linda K. Muthen posted on Monday, June 11, 2012 - 1:27 pm
An empty cell implies a correlation of one. The correlation is not estimated at one and this is the problem. Both variables should not be used in the analysis.
 Thomas A. Schmitt posted on Wednesday, August 22, 2012 - 8:53 am
I'm a little confused by what is being said here. In my case I have: THE BIVARIATE TABLE OF M7 AND M1 HAS AN EMPTY CELL. In traditional categorical data analysis you could put 0.5 in that cell or something of that sort. Is there a way to deal with this in Mplus besides just deleting a variable?

Thanks,

Tom
 Linda K. Muthen posted on Wednesday, August 22, 2012 - 9:23 am
We do add a constant but this does not really solve the problem. An empty cell implies a correlation of one so both variables should not be used in the analysis.
 J.D. Haltigan posted on Wednesday, February 19, 2014 - 11:13 am
Having searched high and low for why my estimates may differ in my IRT models depending on my use of WLMSV vs. MLR I think this may be it.

In the default (WLMSV) mode, I get these warnings for a number of variables. Using MLR I don't. All data is nonmissing (I have no missing data). Does the MLR estimator simply handle the empty cells differently?
 Bengt O. Muthen posted on Wednesday, February 19, 2014 - 11:32 am
ML doesn't first compute latent correlations as in WLSMV, so results may differ a bit when there are zero cells (which hurts correlations). But note also that the default ML link is logit, whereas WLSMV uses probit.
 J.D. Haltigan posted on Wednesday, February 19, 2014 - 12:02 pm
Thank you! Two follow-ups.

1) Most p-values for the indicators (loadings) in the WLSMV (probit) are significant; in MLR (logit) they are not. That said, ICC curves are generally in accord. The one curve that literally reverses its direction is for the indicator that has the most empty cell warnings in WLMSV. As such, is MLR (logit) somehow taking into account the rarity of occurrence for this particular behavior (indicator) differently than probit? More specifically, given the high zero-inflation of the indicators is MLR/ logit a better choice?

2) What fascinates me is that the estimates of the IRT ZIP I ran (count) mimics the results of the MLR IRT run (categorical). Thus, my inclination is that using MLR in the binary case better addresses my data given such rare occurrences of some indicators? Or am I completely off base?
 Bengt O. Muthen posted on Thursday, February 20, 2014 - 2:16 pm
1) I don't think it is clear that ML is better than WSLMV with empty cells. Research with simulations would be needed to shed light on that I can't recall having seen that. - Anyone? I would think ML also suffers from empty cells since you then have limited information about association between pairs of items.

2) I am not sure one can take the count results as support for the binary ML advantage - they may suffer similarly from the empty cells.
 Matt Keough posted on Sunday, March 23, 2014 - 5:19 am
Hi. I am testing invariance across gender using a CFA. The indicators are dichotomous. When I run the configural invariance analysis I get an error message that "the bivariate table has an empty cell." Through reading the forum, I understand that mplus recognizing empty cells as having a tetrachoric correlation of 1. Thus, I tried to trim some items but the problems remains. Could this just be an issue with too many zeros? Is there a way to fix this? Thanks!
 Linda K. Muthen posted on Sunday, March 23, 2014 - 6:28 am
When two dichotomous items have a zero cell in their bivariate table, only one variable should be used in the analysis.
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