

Interpreting coefficients cat > cont... 

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Jen posted on Wednesday, January 24, 2018  8:34 am



Hello, I have browsed many threads related to interpretation with the WLSMV estimator, but I do not think my particular question has been addressed. We have a complex path model with some categorical outcomes, and therefore are using the WLSMV estimator. We are interested in providing more context to a significant path from a categorical variable (U) to a continuous outcome (Y). U is the outcome of other variables and thus appears on the CATEGORICAL list. Therefore, I believe it is represented by an underlying continuous variable U*. What is the best way to help reviewers/readers understand the effect of U on Y? With ML(R), we would probably provide the value of Y for those with U=0 and U=1, but that isn't appropriate here, right? Calculating the value of Y at 1 SD above and below the mean of U* also doesn't seem to make sense since U is categorical and it is hard to explain what a SD means to reviewers/readers. Any suggestions? Thank you! 


Working with U*, you can use the more elaborate interpretation approach of Xie(1989) in SM&R: Structural equation models for ordinal variables; see page 343. But if you prefer to interpret in terms of effects of U, I would suggest estimating the model in those terms, that is, let U and not U* be the predictor of Y. WLSMV cannot do this but it is the default when using ML(R) and can also be obtained using Bayes and Predictor=Observed. 

Jen posted on Wednesday, January 24, 2018  2:12 pm



Thanks for your response. It seems to me that Xie discusses the impact of latent categorical variables on other latent categorical variables. What if the outcome Y is continuous? I generally prefer to stick with MLR, but we needed standard model fit indices and covariances involving categorical variables in this case. I am worried our audience would not accept Bayes, alas. (For anyone viewing this thread in the future, the Xie article is available here: https://scholar.princeton.edu/sites/default/files/yuxie/files/xie1989smr.pdf) 


Then you will have to stick with WLSMV and try to clarify the interpretation of the magnitude of the U* effect on the continuous Y. The model says that this U* latent response variable, rather than the observed U, influences Y. The slope for Y regressed on U* has the usual interpretation; the slope is the effect on Y by U* changing 1 unit. The complication that you are encountering is that you want to know how U* changes relate to U. U* changing 1 unit influences the U=1 probability differently depending on the level of U* (the starting point from which the change takes place).  So to tie different U* values to probabilities of U=1, you can for example compute the mean of U* at the sample means of the predictors of U* and use this U* mean and the residual variance for U* to compute what the probability of U=1 is for the mean and say 1 SD above the mean of U*. Because these 2 probabilities tell you how the propensities for U* relate probabilities for U=1, you can then get a feeling for how U relates to Y. It won't be in terms of U switching from 0 to 1 (that's another model), but perhaps from a low to a high value, or from a moderate value to a high value. 

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