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Hi, I fit a model to my data that includes a significant quadratic trend factor. I am writing my results and want to make sure I am making appropriate interpretations. Is the log odds the sum of the Betas? Regarding my covariate, it's only significant for the linear trend. Would that be interpreted the same as the effect on a simple linear model? I already have the latest Hosmer and Lemeshow book, as well the Agresti text. I'd just like your valuable inisght 

bmuthen posted on Tuesday, December 03, 2002  7:57 pm



Because the odds refers to the dependent variable given a set of covariates (x's), the log odds is the whole righthandside of the equation, beta_0 + beta_1*x_1 + beta_2*x_2 etc  see page 339 of the Mplus User's Guide. So, it is not the sum of beta's alone. The answer to your second question is yes. 


Bengt, I'd like to thank you for being so helpful to all of us who strive to understand structural equation modeling. You are an exellent teacher. The rest of us can only hope to treat others as well as you and Linda do. 


Does anybody know a good source how to interpret the means of the growth factors with ordered categorical variables as dependent variables over time? How can I calculate the mean of the intercept out of the thresholds? 


See the following book: Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (2008). Longitudinal Data Analysis. Chapman & Hall/CRC Press. A good way to interpret this is to look at plots. See the PLOT command. 


Thank you for this help. I ordered the book and had a look at the plots, but I want to make my problem more concrete. I modeled a growth curve with 5 time points and categorical indicators (0,1,2). The means of the intercept and linear slope are 1.303 and .103. Of course, there is an increase in the log odds of not answering category 1 (=0) over time. But how do you interpret the negative mean of the intercept? SUMMARY OF CATEGORICAL DATA PROPORTIONS S1D_N_T2 Category 1 0.907 Category 2 0.090 Category 3 0.003 S1D_N_T3 Category 1 0.876 Category 2 0.119 Category 3 0.006 S1D_N_T4 Category 1 0.867 Category 2 0.130 Category 3 0.003 S1D_N_T5 Category 1 0.806 Category 2 0.193 Category 3 0.001 S1D_N_T6 Category 1 0.821 Category 2 0.175 Category 3 0.004 


Please send your full output and license number to support@statmodel.com. 


I am running a twolevel growth curve model using four latent variables each indicated by three ordered categorical variables (3 categories). I assume the link function here is probit. The time basis variables are linear and quadratic terms for age. I am at a bit at a loss trying to figure out how to convert the coefficients (and variable thresholds?) into probabilities (or some other more meaningful metric) that show the pattern of change in the latent variables by age. Is this a meaningful question or does one just calculate and plot the growth curve using the mean estimates as in the continuous variable case? Thank you. 


I assume that when you talk about four latent variables, you mean one latent variable at four time points. You can compute the estimated means for this latent variable at each time point using the estimated growth factor means and the time scores. To compute the probabilties of the categorical outcomes you need to do numerical integration over the latent variables so that's hard to do. Mplus does not currently provide that. 


Hello, I set up my quadratic growth model as shown below. However, I got this warning (though could not identify any obvious problems using TECH4): WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN GROUP CHINESE IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE Q. Can you help me identify the problem? MODEL: !This is the Chinese group. i s q  YEAR1@0 YEAR2@0.385 YEAR3@0.692 YEAR4@1; i with s; i with q; s with q; !i on gender; !s on gender; !q on gender; MODEL KOREAN: i s q  YEAR1@0 YEAR2@0.385 YEAR3@0.692 YEAR4@1; i with s; i with q; s with q; !i on gender; !s on gender; !q on gender; 


You would have to send your input, output, and data to Support for us to be able to tell. 


Hi again, I spotted the error in my output. There was a correlation between latent variables greater than 1.00, which is illogical. In the Chinese group, the correlations between Intercept, Linear Growth and Quadratic growth (in the standardized solution) were: I WITH S 0.277 0.245 1.128 0.259 Q 0.144 0.301 0.478 0.633 S WITH Q 1.009 0.053 18.900 0.000 The 1.009 is the illogical value. However, setting S with Q @ 1.00 in the MODEL command doesn't yield a logical solution because that refers to setting the covariance (the estimate in the unstandardized solution) to 1.00, not the correlation (the standardized solution) to 1.00. When I set S with Q @ 1.00, the illogical correlation in the standardized solution remains. How do I set S with Q @ 1.00 in the STANDARDIZED solution, or set the negative bound for this estimate to be 1.00? Is it possible to use the "@" command to set standardized estimates rather than unstandardized estimates? Thank you! 


Hi again, in my question, I meant to write: Is it possible to set the lower bound for this estimate to be 1.00? 


You can set bounds for parameters using MODEL CONSTRAINT. However, in your situation I don't believe this is appropriate since the model for Chinese is inadmissible. You should fit a growth model for each group separately. If the same growth model does not fit well for each groups, across group comparisons are not relevant. It may be that the Chinese group cannot be included because they require a different growth model. 


Actually, as a followup, I got the model to converge by centering the loadings for slope (subtracting .5 from all loadings). Thanks! This issue is resolved. 

Meghan Cain posted on Thursday, January 18, 2018  6:38 pm



In reply to Bengt's comment, "To compute the probabilties of the categorical outcomes you need to do numerical integration over the latent variables so that's hard to do. Mplus does not currently provide that." Is this still true? 


I need to see the exact model to say. 

Meghan Cain posted on Friday, January 19, 2018  11:48 am



USEVARIABLES are l1almo l2almo l3almo l4almo l5almo l6almo l7almo dum1intfm dum2intfm dummale dum1eth dum2eth; CATEGORICAL are l1almo l2almo l3almo l4almo l5almo l6almo l7almo (*); MISSING are all .; ANALYSIS: STARTS = 75 15; ALGORITHM = integration; MODEL: int slope quad  l1almo@3 l2almo@2 l3almo@1 l4almo@0 l5almo@1 l6almo@2 l7almo@3; int ON dum1intfm dum2intfm dummale dum1eth dum2eth; slope ON dum1intfm dum2intfm dummale dum1eth dum2eth; quad ON dum1intfm dum2intfm dummale dum1eth dum2eth; 


The estimated probabilities are still obtained only for models without x's. 

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