I have the case example of running a logistic regression with a binomial response variable and a categorical predictor, with data organized in a contingency table. Are there any formal or practical pros/cons for using sampled parameters (e.g. sampled total) vs. unbiased estimates (e.g. a Total calculated from the same dataset with a Horwitz-Thompson estimator)? Would the choice affect the results of the logistic regression?
I really don't known about your context and data, but I hope Kriging estimation (in geostatistics, but it's well also in biology) is a unbiased estimator, multiple regression model (surly with logistic regression) can be applied with this method. Some information or examples can be found in:
http://en.wikipedia.org/wiki/Kriging
http://r-spatial.sourceforge.net/gallery/
Cheers,
Viet
Is your contingency table 3 dimensional (response x predictor x stratum)?
Or is your categorical predictor the variable you intend to define the strata with in the Horvitz–Thompson estimator?
Thanks Gabor, if I got your point, it is 3-D: I have a binary response variable (fruits yes, fruits no) and a categorical predictor "Damages" with 3 states: if the flowers had no damage, damages at T1month or damage only at T2months.
For each combination of the contingency table I have the sampled values, but I also calculated unbiased estimators of these "subtotals" with an Horwitz-Thompson".
But now I'm not sure if for the logistic regression I should use the sampled or the estimated values and if it makes any difference formally and/or practically.
I understand that
you estimated the "fruit yes" probabilities in three groups (T1_damage, T2_damage and NO_damage). In each of this groups you used a sampling method that enabled you to know the probabilities of including each unit in the sample and the weights of the units. You made two estimates: (1) ignoring the weights and probabilities and (2) using the Horvitz–Thompson estimator. You want to compare the three "fruit yes" probabilities.
If my above understanding is correct then
the logistic regression will only give you acceptable odds ratios if the differences among the weights and the selection probabilities are negligible. In this case the unweighted and the HT mean and variance estimates will be practically the same.
Thanks Gabor, now it is quite more clear to me. The only difference with your interpretation is that the adaptive cluster sampling of the individuals with no damages, T1damage etc. was based on a simple random (non stratified) first selection. But basically it does not change too much what you have said.
Since you don´t seem to have a continuous, but categorical (3 categories, no damage, t1 and t2), predictor. I would suggest to use a loglinear approach, or even a simple chi2 analysis (you can do the latter even with an excel spread-sheet)
hope it helps