Correlation structure
Message/Author
 Bo Fu posted on Monday, October 25, 2010 - 4:16 pm
Hi,

My data contains binary variables, multi-normial variables and continuous variables. I'm wondering, in EFA in MPlus, after I identify the categorical variables' group, how the correlation matrix constructed? by which correlation, (tetrachoric, polyserial, pearson, spearman)

Thank you!
 Linda K. Muthen posted on Monday, October 25, 2010 - 4:51 pm
The correlation matrix contains the correlations appropriate for the pair of variables involved, for example, tetrachoric for two binary, Pearson for two continuous, biserial for one binary and one continuous etc.
 Bo Fu posted on Monday, October 25, 2010 - 7:25 pm
Thank you so much!

And, what is used for between categorical and binary variable, categorical and continuous?

Thanks

--Bo
 Linda K. Muthen posted on Tuesday, October 26, 2010 - 8:12 am
I think by categorical you mean ordered polytomous. A polytomous correlation is used for a binary and ordered polytomous variable. A biserial correlation is used for a continuous and ordered polytomous variable.
 Bo Fu posted on Tuesday, October 26, 2010 - 10:30 am
So, different types of correlations are in the correlation matrix, which is for EFA processing. Is that fair, or say appropriate for this analysis?
Because, say variables A1, A2, B1, B2 and C1, C2, where

A1, A2: multilevel categorical;
B1, B2: binary;
C1, C2: continuous
for the correlation matrix,

1 rA1A2 rA1B1 rA1B2 rA1C1 rA1C2
1 rA2B1 rA2B2 rA2C1 rA2C2
1 rB1B2 rB1C1 rB1C2
1 rB2C1 rB2C2
1 rC1C2
1

where rAB is for correlation between A and B.
so, there is three types of correlations involved:
1) polytomous: rA1A2, rA1B1, rA1B2, rA2B1, rA2B2
2) tetrachoric: rB1B2
3) biserial: rA1C1, rA1C2, rA2C1, rA2C2, rB1C1, rB1C2, rB2C1, rB2C2
4) Pearson: rC1C2

Is it meaningful that one correlation matrix contains different correlation based on different criterion, to used as same scale values in EFA?

 Bengt O. Muthen posted on Tuesday, October 26, 2010 - 5:39 pm
Yes, it is. They all have the same scale: -1 to +1.
 Bo Fu posted on Wednesday, October 27, 2010 - 7:15 am
Thank you.

Could you please, do me a favor, give me a link of reference for polytomous correlation? I couldnot find it.

ps: I can find polychoric and polyserial
 Linda K. Muthen posted on Wednesday, October 27, 2010 - 12:16 pm
I should have said:

A polychoric correlation is used for a binary and ordered polytomous variable.

There is no such thing as a polytomous correlation.