# What method is better to model percentage response with each subject measured two times and heteroscedastic error?

The response was calculated as $\frac{Control-Observation}{Control}*100\%$. Raw values of $Control$ and $Observation$ are not available, I have only calculated values. Each value was measured twice. The scatterplot of two measurements is presented at the figure .

As it can be seen, the error is heteroscedastic and depends on the response value. Note, that actually the chance that negative calculated response is really negative is rather smal. So there can be from 0 to 5 (rude score) subjects with really negative values thus all other negatives represent errors of experiment.

The goal of the model is rather predictivity than evaluation of predictors significance. When fitting model, I'll perform variable selection. I have read that logistic or probit regression are good to model percentages, but how to deal with repeated measurements and heteroscedasticity is unknown. Currently I'm going to find moving standard error of experiment and then use corresponding weights in loess (or, maybe, weighted SVM).

1. What method would be more appropriate in the described case? (non-linear flexible methods are preferred)
2. If my suggestion is OK, what weighted non-linear algorithms are available in R?

Upd1: Here is scale-location plot of model response~subject that shows dependent variance of residuals

It is provided just for clarification purposes. My aim is to explain exactly between-subject variability. Thus currently I'm fitting mean (for each subject) values of response with possible predictors, assigning weights to each mean value. I have about 600 possible covariates, though only small number of them (1-5) can be relevant. Here are residuals plots for single best-fit covariate with and without weighting.

Both are awful. Should I continue this direction searching for complete list of relevant covariates?

• might you be misunderstanding the meaning of heteroskedasticity? it is usually taken to mean that the variance of the residual depends on the value of dependent variable, after controlling for covariates. maybe show us a residual plot after you fit a simple linear model with all of your covariates. May 9, 2013 at 13:19
• Maybe so. Though Wikipedia support general definition of heteroscedasticity that is applicable here. In any case, it is clear from the figure that experimental error increase when response decrease. I want to fit such way that regression line should be close to real values with high responses and can be relaxed with low. Becouse residuals in high values are obviously lack of fit while residuals in low values can be simply experimental error which I'd like not to fit to. May 9, 2013 at 19:24
• It could depend on your covariates. Anyway you don't know until you look. May 9, 2013 at 23:44