I would be very appreciative if someone could help me. What I want to do is:
1. Compare two linear multiple regressions. I want to know what coping strategy best predicts burnout. The first model has eight coping strategies. The second has 7 coping strategies (I removed one coping strategy from first model based on the Z statistic).
2. From here I want to test for parsimony using a likelihood ratio test to compare likelihood values of each model based on a chi-square distribution.
I have no idea how to do the second step, which has been recommended by my research supervisor. Does anyone have any suggestions? I am using SPSS.
Thanks!
Julian
I'm sure others will have more experience than me with regression models. I can only advise you how to achieve what you are looking for in the command-line statistical environment R. I find R to be more flexible and up to date than SPSS. Consider switching to R, as it has more possibilities when it comes to the choice of models and plotting.
I also have a question about your choice of models: Why would you do linear regression? I would go for a by-testsubject mixed-effects model.
To answer your question:
To compare the predictive accuracy of two models, you can use Somer's C and DXY. This book (http://www.sfs.uni-tuebingen.de/~hbaayen/publications/baayenCUPstats.pdf) explains how to achieve this in R. Take a look at P. 305.
To perform a likelihood ratio test, do the following. Run your models in R and store your model objects in two variables. Apply the function anova () to the two model objects. Done. Again, Baayen explains this very good in his book, on page 361.
Hello Julian. You said,
"The first model has eight coping strategies. The second has 7 coping strategies (I removed one coping strategy from first model based on the Z statistic)."
I'm not sure what you mean when you say you removed one coping strategy. It sounds like there must be 8 independent groups of individuals, with each group using a different coping strategy. In SPSS, this means you would have to treat coping strategy as a "fixed factor" (for procedures that allow for that), or as 7 indicator variables (e.g., if using the REGRESSION procedure).
Which procedure are you currently using to estimate your models?
What do you mean when you say you removed one coping strategy from the first model? Did you just eliminate one of the 7 indicator variables? Or did you filter out (or delete) the cases of individuals who were using that strategy?
If you eliminated one of the indicator variables for strategy group, you just combined that group with the reference group. If you deleted or filtered cases from the file, you cannot use a likelihood ratio test to compare the models. Like the F-test on the change in R2 for OLS models, the likelihood ratio test for ML models requires that you have nested models estimated using exactly the same cases.
After you clarify some of these things, perhaps someone will be able to give better advice.
Cheers,
Bruce
This is basically what I am doing. I am exploring coping (measured with Brief COPE, which has 14 coping strategies (predictors)) with burnout (measure with the ProQOL...I am actually exploring burnout, compassion satisfaction and secondary traumatic stress) within a workplace. There were 107 responses to my survey, too few to a run a regression. So what I want to do is to get eliminate the coping strategies (the predictors). What I am doing is:
1. Start with univariate analyses i.e. outcome and predictor
2. Candidate predictors are ones that meet criteria e.g. p
Thanks for explaining more clearly what you're doing. First, I suggest that you take a careful look at Mike Babyak's nice article on over-fitting (link below). See also the Stata FAQ on stepwise regression and other related algorithmic methods (second link).
What many authors describe as "hierarchical" linear regression is different in that the researcher or data analyst determines what variables enter or leave the model from one step to the next, with those decisions being driven by theory and content knowledge.
Finally, for OLS regression, the usual method for comparing nested models is an F-test on the change in R2, not a chi-square test or z-test. Is there some reason for not using the usual F-test?
HTH.
http://www.cs.vu.nl/~eliens/sg/local/theory/overfitting.pdf
http://www.stata.com/support/faqs/statistics/stepwise-regression-problems/
My main concern is the few responses you have (i.e. 107), not sure if any sophisticated analysis will provide meaningful results.
Is it possible to use a variable reduction process like principle components or factor analysis (assuming there is a latent construct)? This way you can use the data that was collected.
Otherwise, the likelihood ratio test (LRT) or Wald Test would work as well. I do not know how to do either of them in SPSS for regression nor did I find an answer in the stats books I have. I can give you the actual formula to calculate the log likelihood for regression, and than use the log likelihood to calculate the Chi2 stat for LRT. Not sure how much help that would be for you though.
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