Inga BEck posted on Thursday, August 14, 2008 - 3:05 am
I am planning to use Mplus 5.0 for a twolevel logistic analysis with a binary dependent variable and ML-estimation.
In my model, the predictor variables are situated either on the within-level (x) or the between level (w) only. All within-level effects are fixed (no random slopes). Mplus Manual p. 407 shows how to transform logistic regression coefficient in various ways.
My question is whether these guidelines also apply for calculating odd ratios for between-level (cluster-level) predictors. Other than odd ratios for within-level predictors, such odd ratios are not automatically shown in the Mplus-output.
May I use Mplus-example ex9.3 for illustration. There is an unstandardised b-value of 1.269 for the logistic regression of u on between-level predictor w. W
ould it be correct to transform this coefficient by exp(1.269) = 3.55, meaning that “between clusters, the odds of u = category ‘a’ vs. u = category ‘b’ increase by factor 3.55 for each unit increase in w?
On the between level u is a random intercept. It is a continuous latent variable. The coefficient is a linear regression coefficient. It cannot be turned into an odds ratio.
Inga BEck posted on Thursday, August 14, 2008 - 7:23 am
Ok, thank you. Yet now I have two follow up questions:
Q 1. For the hypothetical model described above, in principle I could also use the stdyx-standardised coefficient of between-level predictor w for interpretation?
Q 2. If I would use WLSMV instead of ML and thus estimate a probit regression, the intercept (threshold)of u would still be considered to be continous and again parameter estimates of between-level predictors would be linear regression coefficients, not probit-coefficients?
Inga BEck posted on Tuesday, August 19, 2008 - 3:07 am
Yet I don't fully understand the Mplus approach to twolevel modeling for categorical data with maximum likelihood (keeping wlsmv aside for a moment).
More specifically, Bryk and Raudenbush (2002, p.300f. ) give an example of a twolevel model with a dichotomous outcome including both level-1 and level-2 covariates.
Here the effects of both level-1 and level-2 covariates are expressed in logit coeffecients and odd ratios.
Obviously, while some statistical perspectives (and software programs used by Bry & Raudenbush, see also the example in the book by Joop Hox) use a logit link for both within- (level 1) and between (level-2) relations, Mplus proceeds in a way that allows for linear regression coefficients on level-2 .
I would be very grateful for more information just how (statistically, technically) Mplus treats varying intercepts (question 1) and slopes (question 2) in a twolevel framework with categorical dependent variable so that one can use linear regression (Not: logit) coefficients.
Question 3: Is there any recommendable literature on this question for applied researchers (perhaps 'below' the level of psychometrika)? Or examples of published articles using the Mplus approach?
Mplus modeling is the same as other programs doing 2-level ML for categorical data - and the interpretations are the same. Good that you gave a specific references to pages in the R & B book, which clarifies our discussion. Page 300 does talk about log-odds, but note that this concerns regression coefficients that appear in level-1. As an example gamma10=-0.492. From equation 10.13, beta1j = gamma10 where beta1j is the fixed slope for SES in the level-1 equation. When we say that level-2 regression coefficients are those of linear regressions (because the dependent variables on level 2 are continuous), we refer to the coefficients gamma00, gamma01, gamma02, and gamma03 in eqn 10.13. In that equation, the dependent variable is beta0j which is a continuous dependent variable and therefore the gamma's are regular linear regression coefficients.
Having clarified that, we see from eqn 10.12 that ultimately beta0j does affect etaij and therefore ultimately does affect the probability of the binary outcome.
So, R & B is a good and sufficient reference for this. I can't remember seeing a less technical one.
Just adding to the previous, when you insert beta0j into the level-1 equation and therefore consider etaij (the log-odds) as the dependent variable, then the gamma0's can be turned into log-odds interpretations. R & B shows an example of that for gamma03. So it is a function of which dependent variable one considers, beta0j or etaij.
Sarah Hall posted on Thursday, September 08, 2011 - 11:32 pm
I am modelling relationships between individual and group level predictors and a binary outcome (using TYPE=TWOLEVEL RANDOM). I would like to plot the significant cross-level 2-way and 3-way interactions as logistic curves. Is it possible to do this in MPlus? I have tried each of the commands: “TYPE is plot1;” “TYPE is plot2;” and “TYPE is plot3;” but these only allow me to create scatterplots and histograms.