I know this has been dealt with before on this list, but the previous messages lacked detail, and I haven't figured it out yet. The model is: \x_{ij} = \mu + \alpha_i + \beta_j \alpha is a random effect (subjects), and \beta is a fixed effect (condition). I have a link function: p_{ij} = .5 + .5( 1 / (1 + exp{ -x_{ij} } ) ) Which is simply a logistic transformed to be between .5 and 1. The data y_{ij} ~ Binomial( p_{ij}, N_{ij} ) I've generated data using this model, and I'd like to fit it. My data is a data frame with 3 columns, "response" (0/1), "subject" (a factor), and "condition" (another factor). Here is my link definition: ############################# halflogit=function(){ half.logit=function(mu) qlogis(2*mu-1) half.logit.inv=function(eta) .5*plogis(eta)+.5 half.logit.deriv=function(eta) .5*(exp(eta/2)+exp(-eta/2))^-2 half.logit.inv.indicator=function(eta) TRUE half.logit.indicator=function(mu) mu>.5 & mu<1 link <- "half.logit" structure(list(linkfun = half.logit, linkinv = half.logit.inv, mu.eta = half.logit.deriv, validmu = half.logit.indicator ,valideta = half.logit.inv.indicator, name = link), class = "link-glm") } binomial(halflogit()) Family: binomial Link function: half.logit ############################# I based this off the help for the family() function. So I try to call glmmPQL (based on other R-help posts, this is the easiest to use?) ################# glmmPQL(response ~ condition, random = ~ 1|subject, family = binomial(halflogit()), data = dat) Error in if (!(validmu(mu) && valideta(eta))) stop("cannot find valid starting values: please specify some") : missing value where TRUE/FALSE needed In addition: Warning message: NaNs produced in: qlogis(p, location, scale, lower.tail, log.p) ################# It looks like I've misdefined something and it is going outside the specified domains for the functions. I can't find any reference to starting starting values in help for glmmPQL() or lme(). If anyone has any working code where they've done a user defined link function, it would be greatly appreciated. Thanks, Richard