

Basic question about 2 x 2 contingenc... 

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Phil Wood posted on Saturday, October 17, 2009  8:27 am



I must have a bit of chess blindness, but wanted to show a colleague a simple case of analyzing a 2 x 2 contingency table with the logit link function. I adapted the following code from a data set in the manual: TITLE: 2 x 2 contingency table DATA: FILE IS ex8.12.dat; VARIABLE: NAMES ARE u1u4 c1c4; USEV = u1u2; CATEGORICAL = u1u2; ANALYSIS: estimator=mlr; MODEL: [u1$1* u2$1*]; u1 on u2; My question: Shouldn't the marginal proportions of the two classes by equal to exp(u1$1)/(1+u1$1) and exp(u2$1)/(1+u2$1) respectively? The estimated values of .081 and .344 yield .52 and .58, and, for these data, Mplus reports .49 and .59. Sorry to bother with such a simpleminded question! 


You want exp(u2$1)/(1+exp(u2$1)). Also, for the marginal of u1 you want to take into account that it is regressed on u2, so not use only the intercept [u1$1]  but that is a bit messy. Alternatively you can turn the u's into equivalent c's and use the loglinear parameterization and c1 WITH c2 and then you get both marginals as the [cj$1]s. 

Phil Wood posted on Saturday, October 17, 2009  2:09 pm



I'm sorry, the formula you give is what I typed in my excel spreadsheet. The .081 and .344 still yield .52 and .58, so what you're saying is that the .59 is within rounding error? The second bit I'm not quite parsing Is what you mean by turning the u's into c's is to make them classes? thanks! 


Yes, make the u's into identical latent class variables  like in the loglinear modeling example 7.15 in the User's Guide. Then you have more modeling freedom to let the variables associate  you can say WITH for two c's but not for two u's in the ML framework.  And you can sometimes handle measurement error in the u's: latent loglinear modeling (I haven't seen anyone pick up on that yet). 

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