Are growth models nested?
Message/Author
 Aurelie Lange posted on Friday, October 21, 2016 - 6:46 am
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?

Sincerely,
Aurelie
 Bengt O. Muthen posted on Friday, October 21, 2016 - 12:55 pm
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.
 Aurelie Lange posted on Monday, October 24, 2016 - 2:02 am
Dear dr Muthen,

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
 Bengt O. Muthen posted on Monday, October 24, 2016 - 10:20 am
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.
 Kiki van Broekhoven posted on Thursday, June 15, 2017 - 6:27 am
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?
 Bengt O. Muthen posted on Thursday, June 15, 2017 - 6:07 pm
I would go with (1).
 Kiki van Broekhoven posted on Thursday, August 03, 2017 - 1:36 am
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?