I am running a multilevel regression analysis using Mplus (with random intercepts and slopes).
In my model, I've entered three continuous level 2 independent variables, two dummy-coded level 1 independent variables and a continuous dependent variable.
My level 2 sample size is only 10 (level 1 sample size is 300). I am using the default estimator, MLR.
The model runs and I get the corresponding output. However, I also get the following error message:
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX.THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS -0.130D-18. PROBLEM INVOLVING PARAMETER 11.
THE NONIDENTIFICATION IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS. REDUCE THE NUMBER OF PARAMETERS.
To what extent (if at all) can I trust my results (If I counted correctly, the number of estimated parameters is 12)?
Thanks for your help!
Boliang Guo posted on Tuesday, October 18, 2005 - 1:43 am
see raudenbush's hlm book, the minmum number of level 2 unit is 30 but he conducted a meta analysis with 19 studies. the number of level2 unit in your study is really small and you are also not lucky to get the good result. can you modle a complex OLS equation with only 10 case? if you have no strong theory background about the between l2 unit variance, then, try ols.
Dear Dr. Muthen I am trying to run multilevel logistic regression analysis, with ML estimator, to identify variables that significantly effect the school type that a child goes to. At the micro level I have child characteristics and at macro level I have family characteristics. I have following questions about the analysis:
1) When I run the null model I get intercept variance at the macro-level but I do not get intercept coefficient. How can I get it? Is threshold the intercept coefficient?
2) Is the fact that my model has only random intercept and no random slope good enough justification (taking into account hierarchical data) for multilevel modelling?
3) Can I use var/s.e. to test if the intercept in null model is random or not. Or will I have to do some other test like fixing variance of intercept to zero and doing likelihood ratio test? Is estimate/s.e. for covariates, variances and covariances z-score or t-value?
Many thanks Joanna p.s. I hope you had great vacation.
one last question I could not post due to post limit.
In order to test model fitness I am using loglikelihood ratio test. What I am doing is I introduce a covariate in the model and record the loglikelihood value and then in the second step I fix the coefficient of that covariate to zero and record second loglikelihood value. Then I multiply the difference (second – first) of two recorded values with -2 and do chi-square test. Is this way correct? Or is there any other way of checking model fitness?
For the LRT, take 2 times the difference in H0 Value from the model fit, and take the difference in model parameters as the df. For example, assume the first model has an H0 = 5237.921, df = 16, and for the second model, if H0 = 5236.561, df = 20, 5237.921-5236.561 = 1.36 * 2 = 2.72, df = 4. Chi-square for df = 4 critical value = 9.488, therefore, chi-square 4 = 2.72 > .05, and the second model is not an improvement over the first model.
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1. Yes. 2. Yes. 3. Yes as an approximation. Because you are testing a variance against zero which is on the border of admissible values, this test may have problems. There is a large literature on this topic.
I think when you test two nested models where covariates values are fixed to zero and where they are free, the test describes the significance of the covariates. I don't think it says that the model with covariates is better.
Dear Linda, Regarding intercept coefficient in multilevel regression. UCLA website has presented example from Snijders and Bosker using MPlus in chapter 14. In all the examples intercept coefficients has been shown by S & B as threshold for dependent variable at between level, but with negative sign. Could you please clarify if intercept coefficient is threshold or threshold with (-) sign? Also, when this intercept coefficient for null model is converted to probability will it be same as proportion of 1 in the dependent variable? Many thanks and sorry about previous post. Joanna
Dear Linda, Following what you told I ran null model with just dependent variable at between level. Results are: Estimates S.E. Est./S.E. Between
Thresholds Q2$1 0.709 0.650 1.090
Variances Q2 34.909 12.985 2.688
From what you told me my intercept coefficient is -0.709. When I convert it to probability of u=1 it comes out as 0.33 where as I have 41.3% observations as u=1 in my sample. Why am I getting this difference? Shouldn't the two probabilites be same? Many thanks Joanna
I am running a "Random Intercept Random Slope with Level 1 & 2 Predictors". My level 2 predictor is the school SES. The DV is fruit intake. I got the following error message: One or more between-level variables have variation within a cluster for one or more clusters. Check your data and format statement.
This is the code that I used:
Within = eat_frontof TV; between= SES;
%within% slope |fruit on eat_TV;
%between% fruit slope on eat_TV; fruit with slope;
Any variable on the BETWEEN list must have the same value for every member of a cluster. Apparently SES does not meet this criterion. If you can't figure it out, please send the output, data, and your license number to email@example.com.