How many degrees of freedom?
Message/Author
 Florian Fiedler posted on Wednesday, June 08, 2005 - 5:23 am
I've got a question concerning the degrees of freedom in a twolevel-analysis. I'm conducting a 2-Level-CFA, incorporating 6 variables and two correlated factors on each level. The output indicates that there are 32 free parameters in the model (I agree to that number). With 6 observed continous variables, how many degrees of freedom does the model have (6*7-32=10?)? According to the MPlus-information in the chi-square test of model fit section I should have 16 degrees of freedom. Where do those 6 dfs stem from or where am I wrong?

Thank you for an explanation.

Regards, Florian Fiedler.
 bmuthen posted on Wednesday, June 08, 2005 - 7:01 am
You should count the 6 means as well - because you work with multivariate normality, the H1 model has 6 means and 2x21 var-covar parameters.
 Sylvie Mrug posted on Thursday, August 02, 2007 - 12:54 pm
I am running a TWOLEVEL model with 3 Level 2 predictors and 1 Level 1 covariate. How can I determine the df for the t-test of each Level 2 predictor? There are 27 Level 2 clusters.
Thanks so much for your help.
 Linda K. Muthen posted on Thursday, August 02, 2007 - 1:00 pm
The ratio of the parameter estimate to the standard error (column three of the output) is a z-score. You can compare it to 1.96 for example.
 Sarah Hall posted on Wednesday, December 14, 2011 - 9:30 pm
Hello,
I am using TYPE=TWOLEVEL RANDOM to model relationships between 1 individual-level predictor and 2 group-level predictors and a continuous individual-level outcome. I need to report the degrees of freedom for each of the effects, but I notice that these are not provided in the Mplus output. What is the formula for calculating degrees of freedom in a multilevel model such as the one I've described?
Thank you!
Sarah
 Linda K. Muthen posted on Thursday, December 15, 2011 - 9:45 am
In a model where means, variances, and covariances are not sufficient statistics for model estimation, degrees of freedom for the chi-square test are not relevant.
 Sarah Hall posted on Friday, December 16, 2011 - 12:08 am
Sorry I should have specified - I am actually trying to obtain the degrees of freedom for the t-tests for each of my effects.
 Linda K. Muthen posted on Friday, December 16, 2011 - 9:15 am
The test we give is a z-test in large samples and does not use degrees of freedom.
 Kätlin Peets posted on Saturday, February 01, 2014 - 2:00 am
Hi,
I am also being told that degrees of freedom should be included in statistics reported in text.

I have two-level models where I test interactions between two contextual variables (thus, interactions are at Level 2). I report results for my simple slopes (at high and low values of the moderator) in the text. What is the correct way to calculate degrees of freedom for my simple slopes? Is it N (number of level-2 units) - number of level-2 variables in the model?

Thank you!
 Linda K. Muthen posted on Saturday, February 01, 2014 - 2:08 pm
The ratio of the parameter estimate to its standard error is a z-test in large samples. There are no degrees of freedom involved with z-tests. Degrees of freedom are involved with t-tests which Mplus does not give.
 Amy Walzer posted on Tuesday, February 11, 2014 - 4:31 pm
In reading the previous posts I see that a z-test is used to test significance in large samples. However, I am doing a two-level model with 2 individual-level predictors and 1 group-level predictor. I have 126 participants among 11 groups. Can this be considered a large sample?

Thank you,

Amy
 Linda K. Muthen posted on Wednesday, February 12, 2014 - 10:50 am
If you have 11 clusters, this is not enough for multilevel modeling. You should create 10 dummy variables and use them as covariates to control for non-independence of observations. In this case, 126 should be enough.