In this work we present a new method for genetic analysis of twin data which is based on generalized estimating equations and allows for analysis of various response types (e.g., continuous, binary, counts) combined with estimation of residual correlations. The new approach allows for control of covariates of any kind (e.g., continuous, counts) by modeling the dependence of mean and variance on background variables. The proposed method was applied to identify the covariates that have a significant influence on elderly people’s functional abilities, and find the estimates for the correlation coefficients of residuals for MZ and DZ twins in a sample of 2401 Danish twin 75 years of age or older. The bootstrap method was used to obtain standard errors for correlation coefficients. It was shown, that the chosen covariates have similar effects on MZ and DZ twins, and that the residual correlation in MZ twins is significantly higher than in DZ twins, which indicates that genetic factors play an etiological role in the determination of physical status of elderly people, controlled for 10 background variables.