The residuals at level \(i\) are obtained by subtracting the fitted
levels at that level from the response vector (and dividing
by the estimated within-group standard error, if
`type="pearson"`

). The fitted values at level \(i\) are obtained
by adding together the population fitted values (based only on the
fixed effects estimates) and the estimated contributions of the random
effects to the fitted values at grouping levels less or equal to
\(i\).

```
# S3 method for lme
residuals(object, level = Q,
type = c("response", "pearson", "normalized"), asList = FALSE, ...)
```

if a single level of grouping is specified in `level`

, the
returned value is either a list with the residuals split by groups
(`asList = TRUE`

) or a vector with the residuals
(`asList = FALSE`

); else, when multiple grouping levels are
specified in `level`

, the returned object is a data frame with
columns given by the residuals at different levels and the grouping
factors. For a vector or data frame result the `naresid`

method is applied.

- object
an object inheriting from class

`"lme"`

, representing a fitted linear mixed-effects model.- level
an optional integer vector giving the level(s) of grouping to be used in extracting the residuals from

`object`

. Level values increase from outermost to innermost grouping, with level zero corresponding to the population residuals. Defaults to the highest or innermost level of grouping.- type
an optional character string specifying the type of residuals to be used. If

`"response"`

, as by default, the “raw” residuals (observed - fitted) are used; else, if`"pearson"`

, the standardized residuals (raw residuals divided by the corresponding standard errors) are used; else, if`"normalized"`

, the normalized residuals (standardized residuals pre-multiplied by the inverse square-root factor of the estimated error correlation matrix) are used. Partial matching of arguments is used, so only the first character needs to be provided.- asList
an optional logical value. If

`TRUE`

and a single value is given in`level`

, the returned object is a list with the residuals split by groups; else the returned value is either a vector or a data frame, according to the length of`level`

. Defaults to`FALSE`

.- ...
some methods for this generic require additional arguments. None are used in this method.

José Pinheiro and Douglas Bates bates@stat.wisc.edu

`lme`

, `fitted.lme`

```
fm1 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
head(residuals(fm1, level = 0:1))
summary(residuals(fm1) /
residuals(fm1, type = "p")) # constant scaling factor 1.432
```

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