CELS error message

Date: Mon, 14 May 2001 15:37:03 -0700 (PDT) From: stuart@c255.ucsf.edu The actual error message is: WEIGHTED SUM OF "SQUARED" INDIVIDUAL RESIDUALS IS INFINITE It is to be understood pretty much at face value. An individual residual is the difference between a response and its individual-specific prediction, (when there are L2 records, the response may be multivariate, and the residual will be a vector difference). A squared individual residual is the square of the residual (when the residual is a vector; it's square is the scalar product of the vector with itself). The phrase "weighted sum" may be confusing. It actually refers to the sum of weighted squared individual residuals. A weighted squared individual residual is the squared residual multiplied by the reciprocal of the intraindividual variance of the residual (when the residual is a vector, the weight is the inverse of the intraindividual variance-covariance of the residual). The sum in question is that sum of weighted squared residuals which ordinarily shows up in the expression for the conditional likelihood for the data from the individual. When can it be infinite? Here are a few possibilities: 1. There is an error in the coding for a prediction, so that the prediction is very large (in absolute value), and along with a very small intraindividual variance, the weighted squared residual is effectively infinite. (E.g. the prediction is a logarithm, whose argument is mistakenly coded so that it is very small.) 2. The prediction is very large due to an incorrect value on the data record containing the response. 3. An initial estimate of an element of SIGMA is mistakenly very small, so that an intraindividual variance is very small, and the weighted squared residual is effectively infinite. 4. A prediction is mistakenly very small and this has the effect of making the intraindividual variance very small (as with a constant cv intraindividual variance model), and so the weighted squared residual is effectively infinite. 5. A intraindividual variance model is being used which legitimately produces a very small variance, but the corresonding residual is not correspondingly small, and the variance model is inappropriate. There are other possibilities, and there can be combinations of possibilities.