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R = residuals(lme) returns the raw conditional residuals from a fitted linear mixed-effects model lme.
R = residuals(lme,Name,Value) returns the residuals from the linear mixed-effects model lme with additional options specified by one or more Name,Value pair arguments.
For example, you can specify Pearson or standardized residuals, or residuals with contributions from only fixed effects.
Conditional residuals include contributions from both fixed and random effects, whereas marginal residuals include contribution from only fixed effects.
Suppose the linear mixed-effects model lmehas an n-by-p fixed-effects design matrix X and an n-by-q random-effects design matrix Z. Also, suppose the p-by-1 estimated fixed-effects vector is $$\widehat{\beta}$$, and the q-by-1 estimated best linear unbiased predictor (BLUP) vector of random effects is $$\widehat{b}$$. The fitted conditional response is
$${\widehat{y}}_{Cond}=X\widehat{\beta}+Z\widehat{b},$$
and the fitted marginal response is
$${\widehat{y}}_{Mar}=X\widehat{\beta}.$$
residuals can return three types of residuals: raw, Pearson, and standardized. For any type, you can compute the conditional or the marginal residuals. For example, the conditional raw residual is
$${r}_{Cond}=y-X\widehat{\beta}-Z\widehat{b},$$
and the marginal raw residual is
$${r}_{Mar}=y-X\widehat{\beta}.$$
For more information on other types of residuals, see the ResidualType name-value pair argument.