'parameters'and'Degrees of Freedom'fo... PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Caoshang posted on Thursday, April 21, 2011 - 7:17 pm
Respect moderator:
when I structure a exploratory LCA,\example as follow:
5 items(binary yes=1,no=0 item1=A,item2=B...item5=E);
MODEL(3-class model,T=3) ŽÍ2(27.677) G2(21.003) AIC(57407.883) BIC(57534.981) df(14) Para(17)
hand couputation:
Number of parameters=(T-1)+T(A-1)+T(B-1)+T(C-1)+T(D-1)+T(E-1)=T(A+B+C+D+E-4)-1=17
Degrees of Freedom=df=(ABCDE-1)-17=14
The result is same with MPLUS5.1 couputation.But i noticed that the number of parameters(17) is bigger than the number of Degrees of Freeddom(14).
Whether we can't get a set of optimal solution because of that. Should I restrict the parameters?(actually,i don't want to restrict them )So my question is if we insist the result, yet the result are reliable???
 Linda K. Muthen posted on Friday, April 22, 2011 - 7:38 am
With five categorical indicators, the number of parameters in the H1 model is 31. This is the number you should be comparing the number of free parameters to. Your model is identified.
 Caoshang posted on Saturday, April 23, 2011 - 7:10 pm
Respect Linda K. Muthen:
Do I understand your meaning is that:
you means the number of parameters(31) in H1 model(unrestricited model) is the sum of 'the number of free parameters(17)'and 'Degrees of Freedom'.
my question is:
1,In my understanding of the past,if we want to get a set of optimal solution, the number of 'free parameters' should less than the number of 'Degrees of Freedom'.Am I wrong about the view?

2,you said 'This is the number you should be comparing the number of free parameters to'what's the meaning?why we should compare the number of 'parameters'and'free parameters' Is it about the identification problem of the model?

Thank for your patience
 Linda K. Muthen posted on Sunday, April 24, 2011 - 10:41 am
The degrees of freedom are equal to the number of H1 parameters minus the number of free parameters in the H0 model. When the number of degrees of freedom is negative, the model is not identified.
 Jerry Cochran posted on Friday, February 07, 2014 - 12:12 pm

Sorry for the really basic question, but for counting parameters estimated in LCA, is there a specific command that will produce that number? I ask because, while I am familiar with counting parameters in SEM, I am not sure in LCA.

Or is it as simple as: (1) counting the estimates and error variances of the observed indicators, (2) multiplying that sum by the number of classes, and (3) adding 1 for the latent disturbance?
 Bengt O. Muthen posted on Friday, February 07, 2014 - 2:01 pm
The number of parameters is given in the output. For categorical outcomes it is computed as C*T + C-1, where C is the number of classes and T is the number of thresholds (that is, categories minus 1) for each variable.
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