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Are growth models nested? |
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Dear Dr Muthen, I was wondering whether a growth model with only a linear slope is nested in a model including a linear and quadratic slope. I.e., could these two models be compared using the chi-square test? Or should I use AIC and BIC for model comparison? Thank you for your advice! Sincerely, Aurelie |
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If the quadratic slope has zero variance (but non-zero mean) you can use the chi-2 difference test. With free variance, the variance=0 precludes correct chi-2 diff testing. Using AIC or BIC is good. |
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Dear dr Muthen, Thank you for reply. What about adding a dependent variable (y) to the between-level in M1? This variable is already a dependent variable on the within level in the M0. %within% m on x1; y on m x1; %between% m on x2; y on x2; !NEW PATH Is there a 'rule of thumb' to know when models are nested? Or is there some way to check this in the output? thank you! Cheers, Aurelie |
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If M0 has a variance of y on Between then it is nested within M1 which adds a path. M0 simply says that y on x2 = 0. There is a 2010 Psych methods article by Bentler and Satorra that describes a method for checking nesting. |
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Dear dr Muthen, With my GMM (default settings with regard to growth factor variances), I received a warning message with the 4-class model related to a not positive definite PSI. I followed your advice, posted in another thread, of constricting the variance of the slope @0 because my slope variance was not significant for the 4-class model. After that, the error message indeed disappeared. However, for the 1-class and 2-class default GMM models, I did have significant slope variances (for the 3-class model I did not). With regard to reporting the results in my paper, I wonder whether I should report: (1) 1-class, 2-class and 3-class results for the models with default settings regarding growth factor variance; and 4-class results for the model with s@0 (because I first received the error message for the 4-class model) or (2) reports results for ALL models with s@0, so starting from the 1-class model. (sidenote: BIC is very comparable for default models and models with s@0, for all classes) I feel like this question might be related to models being nested; I believe these models are not nested and as such I should start with the 1-class model with s@0 and report those results (so my guess is that I should use option (2)). Am I right? |
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I would go with (1). |
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Thank you for your reply. I am still wondering if, when I go with (1), it would not be wrong to report e.g. the LMR-LRT and BLRT values for a 3-class versus 2-class model, as I worked with s@0 for the 3-class model whereas I did not constrict the slope factor variance for the 2-class model. Because when I ask for the output of TECH11 and TECH14 for the 3-class s@0 model, it compares this model with a 2-class s@0 model, right? How should I deal with this, as I used a 2-class model without the constricted slope factor variance? Thank you in advance. |
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As for your first paragraph, I think it would be wrong. I would simply use BIC. |
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