Troubleshooting
Problem
I have been working on AMOS to analyze a structural equation model. I have been trying to verify the calculation of degrees of freedom for the chi-square test. Specifically, I cannot understand how sample moments are determined. The model has 14 variances 33 regression weights 21 covariances 7 means 7 intercepts equalling 82 free parameters. The calculation of df is 119 - 82 = 37. How was the value of 119 determined? In general, what is the formula for the calculation of the number of distinct sample moments?
Resolving The Problem
In general the number of degrees of freedom equals:
DF = Number of sample moments - Number of free parameters in the model.
From your question, I understand that you have 14 observed variables and that you have requested a model with means and intercepts. For K observed variables, the number of unique elements in the sample covariance matrix is K*(K+1)/2, comprised of K variances and K*(K-1)/2 covariances. For 14 observed variables, this equals 14 variances and 14*13/2 = 91 covariances for a total of 14+91=105 unique values in the sample covariance matrix. (There are 14*14=196 total elements in the covariance matrix, but the matrix is symmetric about the diagonal, so only 105 values are unique). Add the 14 sample means and you have 105+14=119 sample moments. If there were multiple groups in the model (as in Example 12 in the AMOS 4 User's Guide), then you would multiply the number of moments per group (variances, covariances and means (if means are requested in model)) by the number of groups.
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Modified date:
16 June 2018
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