There is no need for every variable in the model to be statistically significant. In fact, the Manuscript Checklist at the link below says that a model with no non-significant explanatory variables is suspicious.
http://biostat.mc.vanderbilt.edu/wiki/Main/ManuscriptChecklistHere's the relevant section:
Lack of insignificant variables in the final modelUnless the sample size is huge, this is usually the result of the authors using a stepwise variable selection or some other approach for filtering out "insignificant" variables. Hence the presence of a table of variables in which every variable is significant is usually the sign of a serious problem.
Authors frequently use strategies involving removing insignificant terms from the model without making an attempt to derive valid confidence intervals or P-values that account for uncertainty in which terms were selected (using for example the bootstrap or penalized maximum likelihood esetimation). A paper in J Clin Epi March 2009 cited Ockham's razor as a principle to be followed when building a model, not realizing that parsimony resulting from utilizing of the data at hand to make modeling decisions only seems to result in parsimony. Removing insignificant terms causes bias, inaccurate (too narrow) confidence intervals, and failure to preserve type I error in the resulting model's P-values, which are calculated as though the model was completely pre-specified.
HTH.
joesturgis wrote
Hello, I'm at a similar place in my research using logistic regression. I have four parameters that fail the linearity test, and was able to use the methods in Menard (1995) to discover possible parametric forms. One is a cubic, and the other three are quadratic; each provides a significant change in -2LL, so I believe all of the forms are correct.
I have one small issue, when I refit the logistic regression with the transformed parameters, one of the quadratic parameters was no longer significant. I can just remove the squared term to get acceptable results, but it doesn't seem right--the other two quadratic parameters are significant and each variable has the same physical meaning. Any suggestions? Could this be a problem with colinearity?
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/"When all else fails, RTFM."
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