My binary logistic regression analysis (method=ENTER) model has all beta values are statistically non-significant.
Should I include these predictors in the final binary logistic regression equation?
Solved – binary logistic regression analysis (method=ENTER) model has all beta values are statistically non-significant
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It depends whether you are doing... a) predictive research, where you don't care about what is causally responsible, only what serves as an efficient set of indicators, or b) explanatory research, where you want to disentangle causal relationships as much as you can.
In the latter, when multiple correlated predictors vie for a role in your equation, you would care about such things as giving "causal credit" to earlier factors over later ones, since what comes later could never cause what came before, but sometimes the reverse is true. You would care about giving more "credit" to relatively objective, relatively fixed variables such as marital status or ethnicity than to relatively subjective, changeable ones such as attitudes and opinions. And (and here I'm paraphrasing James Davis's The Logic of Causal Order) you would want to choose more generative factors such as socioeconomic status over less generative ones such as what brand of toothpaste a person uses.
When your candidate predictors are correlated, no statistical algorithm (such as a stepwise regression) can deal with these issues of explanation. It is up to you as a researcher to think through your candidate variables and choose those that will best serve your purpose. It is only in pure predictive research that you can ignore such issues and simply choose those predictors that account for the most variance in the outcome--or, in your case, produce the highest pseudo-r-squared.
Your question gets to the heart of important issues in multivariate modelling of many types, and if more than 5 tags were allowed I would have also listed multicollinearity, model-building, and/or variable selection.
There are several reasons (none of which are specifically related to logistic regression, but may occur in any regression).
- Loss of degrees of freedom: when trying to estimate more parameters from a given dataset, you're effectively asking more of it, which costs precision, hence leads to lower t-statistics, hence higher p-values.
Correlation of Regressors: Your regressors may be related to each other, effectively measuring something similar. Say, your logit model is to explain labor market status (working/not working) as a function of experience and age. Individually, both variables are positively related to the status, as more experienced/older (ruling out very old employees for the sake of the argument) employees find it easier to find jobs than recent graduates. Now, obviously, the two variables are strongly related, as you need to be older to have more experience. Hence, the two variables basically "compete" for explaining the status, which may, especially in small samples, result in both variables "losing", as none of the effects may be strong enough and sufficiently precisely estimated when controlling for the other to get significant estimates. Essentially, you are asking: what is the positive effect of another year of experience when holding age constant? There may be very few to no employees in your dataset to answer that question, so the effect will be imprecisely estimated, leading to large p-values.
Misspecified models: The underlying theory for t-statistics/p-values requires that you estimate a correctly specified model. Now, if you only regress on one predictor, chances are quite high that that univariate model suffers from omitted variable bias. Hence, all bets are off as to how p-values behave. Basically, you must be careful to trust them when your model is not correct.
Best Answer
In general if a test for the regression coefficient being statistically significantly different from 0 cannot be rejected it suggests that the variable has little influence on the outcome and hence should not be included. However, it could be that the sample size is small and hence the variance of the estimate of the regression coefficient is too large to exclude the possiblity that it is zero. So the question then becomes how much bigger than 0 do I need the coefficient to be for me to want to include it in the model. Then figure out how large a sample size you need to detect a difference from 0 of at least that magnitude. If the sample size is large and all the estimates are close to 0 then exclude them and look for other predictors that might be better. But if the sample size is small and say a 95% confidence interval for a predictor is wide enough to include 0 and your significantly high slope parameter then consider increasing the sample size before you decide.