I ran an experiment with a 2x2 design, like the dependent variable I have a dichotomic variable. When I running a factorial ANOVA, interaction is significant and one principal effect, also when I running a multiple regression, but when I run a logistic regression, every p-value is .998.
when I analyze each variable separately, these are significant again.
Dear Leonardo,
In principle, understanding the nature of your dependent and independent variables are crucial. If your dependent variable is dichotomized and independent variables have two categories, we principally run chi-square test with 2x2 tables. When your independent variables have 3 categories or more, you may run binary logistic regression. One of the principal aim of doing a logistic regression analysis is to obtain the so called "predictor model" of the factors associated with your main outcome. It functions to remove any potential confounders, although potential confounders could be detected early at the design stage. Variable selection into the logistic model is important. In the current statistical methodology interpretation, it is discouraged to adopt the technique of variable selection into the model by utilizing the somewhat "blind method." For example, pulling variables which are statistically significant at the univariate model into the logistic model and running the analysis using Enter, Backward or Forward regressions. Instead, we utilize a systematic method of variable selection. One such technique is the DAG method. These techniques gives you more reliable estimates.
I think that I may understand your question. From the title of your post, is it your concern that when you use the variables separately as predictors you get significant ps, but not when they are all in the model? If so, I expect that what you are seeing is the effect redundancy. With each variable as a single predictor you have its total predictive performance (whether LR or an alternative modeling technique), on the other hand, assuming predictors are correlated, which would in general be the case, the effect (thus p-value) you are observing for each predictor is the increment to prediction performance due to that variable over-and-above that available from the remaining predictors.
Indeed, adding multiple variables, if they have a certain amount of correlation among themselves, the new (additional) information provided (besides the first, second regressor etc) would be minor and thus not necessarily significant, whereas alone, they may be of sufficient important as to be significant.
I think,that it belongs to use variables separately or to put variables in the model.
If I understand your question your first regression was with OLS. THAT IS WRONG. If the DV is binary use logistic regression. the rest of your model is the same as any 2x2 Factorial model. That would be the correct analysis. Best, David Booth
David Eugene Booth :-) I must confess that I never totally understood this question, but it seemed to me that it might have had to do with the frequent confusion between the bivariate relationship of variables to a DV and the contribution of variables to prediction of the DV within a model. Therein, it doesn't mater what model one uses, the fundamental issue is the same. However, as I say, it may be that I have missed the meaning of the question.
What I would like to point out, however, is that if the DV is dichotomous, predicting it with an OLS regression model produces weights that are exactly proportional to (and therefore mathematically derivable from), the discriminant analysis weights originally introduced by Fisher when he invented that technique. [This is the "linear" model; this relationship does not hold for the quadratic model.] So, while one may prefer LR to DA, and for me, this is an empirical question specific to the data set, I would not agree that DA is WRONG.
Thanks for the dialog and my best,
John
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