a simple identifiaction problem PreviousNext
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 LR posted on Monday, March 04, 2013 - 5:39 pm
In the path model which is discussed here:
http://www.ats.ucla.edu/stat/mplus/seminars/introMplus_part2/path.htm
there are 4 observed variables. Cursory inspection tells me that there should be 1 model degree of freedom: 5*4/2=10 available DF, and 9 estimated parameters. However, the "Degrees of Freedom" is reported by Mplus as 0.

Could you explain what has happened here ?

Thanks !!
 Linda K. Muthen posted on Monday, March 04, 2013 - 9:42 pm
The model is just-identified. The sample statistics for the dependent variables are two means, two variances, one covariance, and four covariances between the dependent and independent variables for nine total.
 LR posted on Monday, March 04, 2013 - 10:20 pm
Thanks Linda. I also worked out nine total DF used. But I thought there were 10 available: 5*4/2=10, leaving 1 free ? Where is my logic going wrong ?
 Linda K. Muthen posted on Monday, March 04, 2013 - 10:51 pm
You are assuming all variables are dependent variables. The degrees of freedom are calculated differently when there is a combination of dependent and independent variables. In the model you refer to both the H1 and H0 models have nine parameters resulting in a just-identified model with zero degrees of freedom.
 LR posted on Tuesday, March 05, 2013 - 4:52 am
Thanks again Linda. Could you indulge me and explain how this calculation of 9 available DF (free parameters) is done ?
 Linda K. Muthen posted on Tuesday, March 05, 2013 - 12:33 pm
The sample statistics for the H1 model are
two means, two variances, one covariance for the two dependent variables, and four covariances between the dependent and independent variables for nine total parameters.
 Linda K. Muthen posted on Tuesday, March 05, 2013 - 1:46 pm
If you want to treat all of the variables as dependent variables, the model still has zero degrees of freedom. The H1 model has 4 means and 10 variances and covariances for a total of 14 parameters. The H0 model has 2 means, 2 variances, and one covariance for the exogenous variables and 2 intercepts, 2 residual variances, and 5 regression coefficients for the endogenous variables for a total of 14 parameters and zero degrees of freedom.
 LR posted on Wednesday, March 06, 2013 - 10:54 am
Hi Linda, and thanks again.

I know what has caused my confusion. Mplus does not output the covariance between the exogenous variables. If hs with col; is added to the model, Mplus very helpfully outputs 14 estimates so the model can easily be seen as saturated, and all original estimates are unchanged.
 Linda K. Muthen posted on Wednesday, March 06, 2013 - 12:57 pm
The reason Mplus does not give the means, variances, and covariances of the observed exogenous variables is that in regression the model is estimated conditional on these variables. When you include them in the MODEL command, you treat them as dependent variables and distributional assumptions are made about them.
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