Polyserial vs. biserial correlations PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Anonymous posted on Wednesday, March 02, 2005 - 8:41 pm
I am testing a 3 factor measurement model. The first factor contains 3 continuous indicators and the next two have dichotomous indicators (5 in one, 3 in the other).The model fit is adequate. When examining the correlation matrices generated from SAMPSTAT, we noticed that they are different from the ones generated using the same data set in SPSS. We think that the issue is that the correlations generated in SPSS are biserial (for the dichotomous variables), while the one's in MPlus are polyserial.

I haven't found a way to request polyserial correlations in SPSS, so wanted to find out how to get correlations in MPlus that are flagged for significance. I tried adding "with" statements between each of the indicators after the model command, but the estimates are still very different from what I got in SPSS. Any suggestions would be greatly appreciated.
 Linda K. Muthen posted on Wednesday, March 02, 2005 - 8:51 pm
With SPSS, Pearson product moment correlations are computed for all pairs of variables. For two binary variables, this is the phi coefficient. SPSS and Mplus will not agree in this instance. In Mplus, the correlation estimated depends on the type of variables involved. For example, you will get a tetrachoric correlation for two binary items, a polychoric correlation for two ordered polytomous items, etc. If you ask for TYPE = BASIC in the ANALYSIS command without a MODEL command, you will get correlations and their standard errors.
 Anonymous posted on Wednesday, March 02, 2005 - 9:57 pm
Thanks Linda. That's helpful. Using type = BASIC, how do you know which of the correlations is actually signficant?
 Linda K. Muthen posted on Wednesday, March 02, 2005 - 11:39 pm
You get the correlations and their standard deviations. An approximate test of significance is to divide the correlation by its standard deviation and compare to 1.96 for example.
 Miho Tanaka posted on Monday, May 07, 2012 - 11:20 pm

I used the above-mentioned method to create correlation martrix for my variables. I have 17 variables. Some of them are continuous variable and others are categorical. In the syntax, categorical variables are spelled out under "categorical are." I am wondering if I am computing polychoric correlations. Or the correlations shown in Mplus matrix are a mixture of polychoric and Pearson's correlations? I appreciate your advise
 Linda K. Muthen posted on Monday, May 07, 2012 - 11:25 pm
The following correlations are used:

binary/binary tetrachoric
ordinal/ordinal polychoric
cont/cont Pearson
binary/cont biserial
ordinal/cont polyserial
binary/ord polychoric
 Tracy Witte posted on Monday, September 16, 2013 - 2:05 pm
I am trying to get significance tests for correlations between a set of observed variables. A couple of questions:

1) When I use "type=basic" in the analysis command, I get correlations, covariances, and means. However, I don't see standard deviations or standard errors for the correlations. Is there a way to request these?

2) Are these correlations calculated using FIML to handle missing data?
 Linda K. Muthen posted on Monday, September 16, 2013 - 5:10 pm
1. Try the H1SE option of the OUTPUT command.

2. If you are using a maximum likelihood estimator, the default is to use all available information and FIML.
 Tracy Witte posted on Tuesday, September 17, 2013 - 1:40 pm
Thanks! When I include the H1SE option of the output command, I get S.E's for the covariances, but not for the correlations. If the covariance/SE is > |1.96|, does that mean that the correlation is also statistically significant?
 Linda K. Muthen posted on Tuesday, September 17, 2013 - 2:12 pm
No, the significance of the covariances does not apply to the correlations.
 Tracy Witte posted on Tuesday, September 24, 2013 - 1:33 pm
So then is it safe to assume that there is no way to ascertain whether the correlations are statistically significant when using the Type=basic analysis?

Additionally, would it be appropriate to present results in a manuscript for the correlation values, and indicate which of these had covariances that were significantly different from 0?
 Linda K. Muthen posted on Tuesday, September 24, 2013 - 5:29 pm
We don't give standard errors for the correlations. It is the covariances that the model is fit to.

The journal usually dictates what is presented and how. Perhaps you should pose this issue on a general discussion forum like SEMNET.
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