Hello all,
I've got a rather complex question concerning my regression.
My data has the following properties.
My goal was to quantify how well my independent variable predicts my dependent variable.
Based on the data properties i must run a generalized linear mixed model with negative binomial distribution and log link function with random intercept for groups.
Now, at first my idea was to calculate how much of the explained variance in the dependent variable can be attributed to the independent variable using SPSS. So far, i could only find a possible analysis in R using the lme4 package. But since i do not work with R this is not an option.
Due to the data properties the explained variance can not be calculated in SPSS i am now looking for a way that comes as close to such an analysis. Pseudo-r-squareds aren't an option either.
A likelihood ratio test is possible in SPSS, however for this i must run a generlized linear model which means i would ignore the fact that the my data is clustered.
Does anyone have thoughts on this?
Kind Regards,
E
Given the properties of your data, it is important to account for the clustering of the data within groups. Ignoring the clustering could lead to biased estimates of the standard errors and confidence intervals. While SPSS does not have built-in functions for fitting generalized linear mixed models, there are some workarounds that you can consider.
One option is to use a different statistical software that can fit generalized linear mixed models, such as R or SAS. Alternatively, you can use SPSS to fit a generalized linear model, which ignores the clustering, and then adjust the standard errors and confidence intervals using a sandwich estimator. The sandwich estimator is a robust method that accounts for clustering and is suitable for use with overdispersed count data.
To calculate the amount of variance explained by the independent variable, you can use the adjusted R-squared. Although the adjusted R-squared is not a true measure of explained variance in the same way as in linear regression, it can still be informative in assessing the goodness-of-fit of the model. Additionally, you can use the likelihood ratio test to compare the fit of a model with and without the independent variable. The likelihood ratio test can provide an indication of whether the independent variable is a significant predictor of the dependent variable, while accounting for the clustering of the data.
Thank you for your response. I am not very familiar with the sandwich estimator so that would require some research but your answer sounds very promising.
So first, I can run a generalized linear model without taking account clustering.
Can i already choose the option to measure the adjusted r squared and likelihood ratio in this first analysis. Or should i run a second analysis? And do the estimates for adj-r-squared and likelihood ratio loose their power because clustering is not included in the initial analysis?
A simple and flexible approach for pseudo r-squared is Efron's pseudo r-squared, explained here ( https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/ ), substituting π in the formula with the predicted values.
All you need are two out of three of the following: predicted values, observed values, or residual values.
This should be easy to implement in any software.
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