You didn't provide any information about the nature of your response variable, but it sounds like it might be positively- or at least nonnegatively-valued. Such responses could be modeled using a generalized linear model using various distributions. If it is a discrete count response, then you could use the Poisson distribution (or negative binomial if it exhibits extra variability or excessive zeros). If it is continuous and positive, then the gamma, inverse Gaussian, or Tweedie distributions are commonly used. With these distributions, it is common to use the log link function to model the log of the distribution mean.
But yes, if your subjects or items are repeatedly measured, then the implied correlation should be taken into account by using an appropriate model such as a Generalized Estimating Equations model (PROC GEE) or a random effects model (PROC GLIMMIX) depending on the purpose of the model. Both procedures can use distributions like Poisson and gamma. See the examples in the documentation of those procedures. Also see this note on modeling positive, continuous responses and this note on modeling count responses using various distributions (though this is primarily about handling overdispersion).
