I suggest to look for more recent papers on the subject, e.g. in PubMed: http://www.ncbi.nlm.nih.gov/pubmed

Examples:

Article Why Match? Investigating Matched Case-Control Study Designs ...

Article Case–control matching: effects, misconceptions, and recommendations

https://academic.oup.com/aje/article/190/9/1859/6162924

In multiple regressions (even higher order non-linear least squares regressions, the degrees of freedom (DF) is equal to the number of independent observations minus one, minus THE NUMBER OF PARAMETERS (p).

DF = n-p-1

This is why some people use DF=n-2 for linear curve fits.

If you increase the number of parameters in the model being fit, then the DF goes down. If the added parameter fails to reduce the residual mean squared error, then the model with the extra parameter will be statistically worse than the model without it. This, itself, is a statistical test for Okham's razor. see Zar, Biostatistical Analysis, under multiple regressions.

Luke V Schneider

Dear Dr. Schneider,

Thank you very much for your invaluable opinions.

Based on what I understood, some of my interpretations will be as follows:

Generally, when we want to estimate the effect of a specific exposure using multiple linear regression, we should include all variables that are obviously associated with the outcome, whether they are confounders. subsequently, the sum of squared errors (SSE) reduces, and the precision of the estimated effect and the statistical power increase.

However, we should note that fitting the statistical model with a large number of parameters can result in the overfitting phenomenon and reduction of the degree of freedom (n-p-1). Then, considering the possibility of the parameter weakness for reduction of residual mean squared errors (RMSE), the model with them will not be statistically suitable.

I hope they are acceptable; however, I would appreciate receiving further comments.

Best regards,

Article Strengthening the Reporting of Observational Studies in Epid...