Computes diagnostics for detection of outliers and influential data points given residuals and the R matrix for a fitted general linear model.

The multiple regression model used by routine ROTIN is

where y is the n × 1 vector of responses, X is the n × p matrix of regressors, β is the p × 1 vector of regression coefficients, and ɛ is the n × 1 vector of errors whose elements are independently normally distributed with mean 0 and variance σ2/wi. The model used by ROTIN also permits linear equality restrictions on β. From a multiple regression model fit using the wi’s as the weights, routine ROTIN computes diagnostics for outliers and influential cases. Let xi be a column vector containing elements of the i-th row of X. Let W = diag(w1, w2, …, wn). The leverage is defined as

(In the case of linear equality restrictions on β, the leverage is defined in terms of the reduced model.) Put D = diag(d1, d2, …, dp) with dj = 1 if the j-th diagonal element of R is positive and 0 otherwise. The leverage is computed as hi = (aTDa)wi where a is a solution to RTa = xi. The computation of the remainder of the case diagnostics follows easily from their definitions. See the Diagnostics for Individual Cases section in the chapter introduction for definitions of the case diagnostics.

The type 3 informational errors can occur if the input variables X, R, E and SSE are not consistent with each other or if excessive rounding has occurred in their computation.The type 3 error message with error code 2 arises when X contains a row not in the space spanned by the rows of R. An examination of the model that was fitted and the X for which diagnostics are to be computed is required in order to insure that only linear combinations of the regression coefficients that can be estimated from the fitted model are specified in X. For further details, see the discussion of estimable functions given by Maindonald (1984, pages 166‑168) and Searle (1971, pages 180‑188).

A multiple linear regression model is fit and case statistics computed for data discussed by Cook and Weisberg (1982, page 103). The fitted model is

Some of the statistics in row 6 of the output matrix OTIN are undefined (0.0/0.0) and are set to NaN (not a number). Some statistics in row 4 of OTIN are infinite and are set to machine infinity. The values of NaN and machine infinity can be retrieved by routine AMACH (or DMACH when using double precision), which is documented in Reference Material.

In this example, routine RNLIN is first invoked to fit the following nonlinear regression model discussed by Neter, Wasserman, and Kutner (1983, pages 475‑478):

Then, ROTIN is used to compute case diagnostics. In addition, the leverage output by ROTIN is used to construct asymptotic confidence intervals on the mean of the nonlinear regression function evaluated at xi. The asymptotic 95% confidence intervals are computed using the formula:

where hi is the computed leverage, t.975,DFE is the 97.5 percentile of the t distribution with DFE degrees of freedom as computed by routine TIN (see Chapter 17, “Probability Distribution Functions and Inverses”), and s2 equals SSE/DFE.