In a multilevel logistic regression, one explanation of a statistical nonsignificant value ((P>.05) is that the confidence interval includes zero. However, I have an SPSS report that where nonsignificant values do not include zero. None of the variables (sig or not sig), have zero in the confidence intervals. A footnote states that the reference category is 1. There are also significant values with a CI that includes 1, so interpreting the statistical significance in any way that includes an examination of the CI doesn’t seem to apply. Also, is a multilevel logistic regression (not binary, more than two dependent categories) the same as a multinomial regression?
It is difficult to answer without being able to see the output. A multilevel, multinomial logistic regression is similar conceptually to a multinomial logistic regression that is not conducted using nested data. The reference category is likely a statement about your dependent variable (i.e., which level is being compared to the rest in the multinomial logistic model). The confidence intervals are in reference to the exponentiated coefficients, not the coefficients themselves. Zero is not a possible value of an exponentiated coefficient (i.e., odds ratio). What is a bit strange to me is that you have statistically significant coefficients that have confidence intervals containing 1. An odds ratio of 1 means that variation in the predictor is unrelated to a reliable change in the odds of being in a given group relative to the reference group. My only thought is that the intervals that include 1 and are otherwise significant are just rounding issues (i.e., printed as 1.000 in the output but really .99997574 or 1.00023761). If you double click on the SPSS output table, you should be able to view the values carried out to additional decimals to see if that is what is going on in this case.
If you look at toothbru freq=1 (2nd highlighted), on the adjusted OR (right side), it says sig., the Std Error (which looks like it might be the B [exp] (don't understand the column header), and interval is 0.846 to 3.127. Why, if its significant?
I actually don't see a coefficient in the table you posted. Is that a table that represents the random effects in the model (specifically their variance)? If so, it may be that you are looking at a table that determines whether there is significant variability in your random effects. If I am right the 95% confidence interval could be an expression about the distribution or variance of odds ratios... (though I have to be honest in that such a confidence interval seems a little strange to me to care much about). Not to cast aspersions on SPSS, but I will say it is not the tool most investigators use for multilevel modeling (SAS proc mixed, HLM, Mplus, and R packages: lme4 & nlme are all probably more commonly used for these sorts of models).
Perhaps if there is someone with more specific SPSS knowledge related to these models they can better address your question. Or if there is more output/syntax you could provide that can help eliminate alternative explanations for these oddly significant values.
Thanks. It's not my analysis. It's a submission that I'm trying to evaluate. I've found a recent paper that provides a goodness of fit: Article A Goodness of Fit Test for the Multilevel Logistic Model
That's all the output the author provided. I've asked for the goodness-of-fit information.
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