I am attempting to explain a dichotomous outcome variable using a large set of continuous valued sensor-derived variables. Many of these variables are highly mutually correlated, some are based on solid physical concepts (and therefore easier to interpret) others are more abstract and difficult to explain.
I am attempting to examine the association of these sensor variables with the outcome (i.e. which variables or combination of variables can best explain the dichotomous outcome variable?) a secondary objective is to determine if a subset of these variables can be used to explain the dichotomous outcome.
I wish to avoid using a stepwise fitting procedure (due to the danger of overfitting and, a feeling that the more easily interpretable variables should be given preference in the model over highly correlated but less easily interpretable variables). In short, I am looking for the true associations rather than noisy surrogates using correlated but less globally informative variables.
To avoid multicollinearity in the analyses, I reduced the number of variables using logistic regression by block analysis. Sensor derived variables were grouped by type into blocks. The dichotomized outcome variable was used as the dependent variable in each sub-group. Working with each block, I performed a logistic regression on each independent variable and only those which were significant (α < 0.05) were retained in each block. Through this procedure I excluded all non significant variables from the analyses for the final model. I then generated a final logistic regression model using the results of each sub-group analysis.
I would great appreciate opinions as to whether this is a valid approach? Can the odds ratios from the final logistic regression model can be used to interpret the associations of the included sensor variables with the outcome variable in the manner of a hypothesis test?