wald: Wald Test of a General Linear Hypothesis for the 'Fixed'...
In john-d-fox/gspline: Generalized Regression Splines

Description Usage Arguments Details Value Author(s) See Also Examples

General Linear Hypothesis with Wald test for, e.g., lm, glm, lme, nlme and lmer objects. Can be extended to other classes by writing an appropriate getFix method.

wald(
  fit,
  L. = "",
  clevel = 0.95,
  p.adjust = "holm",
  adjust = c("all", "each"),
  pred = NULL,
  data = NULL,
  debug = FALSE,
  maxrows = 25,
  full = FALSE,
  fixed = FALSE,
  invert = FALSE,
  method = "svd",
  df = NULL,
  pars = NULL,
  tol.df = 1e+06,
  tol.qr = 1e-10,
  ...
)

## S3 method for class 'wald'
print(x, round = 6, ...)

## S3 method for class 'wald'
as.data.frame(
  x,
  row.names = NULL,
  optional,
  se = 2,
  digits = 3,
  sep = "",
  which = 1,
  ...
)

`fit`	a model for which a `getFix` method exists.
`L.`	a hypothesis matrix or a pattern to be matched or a list of these.
`clevel`	level for confidence intervals. No confidence intervals if `clevel` is `NULL`.
`p.adjust`	a method to adjust p-values for simultaneous inference, using the `p.adjust` function. The available methods are in `p.adjust.methods`, and the default is `"holm"`. To suppress adjusted p-values, specifcy `p.adjust="none"`.
`adjust`	if `"all"` (the default), and `p.adjust` isn't set to `"none"`, then when there are multiple hypothesis matrices, the overall test for each hypotheses is adjusted for all of the hypotheses and the p-values for the individual hypothesis parameters are adjusted across all of the hypotheses; if `"each"` then the p-value for the overall test for each hypothesis isn't adjusted and the p-values for the individual parameters are adjusted separately for each hypothesis matrix.
`pred`	(default `NULL`) a data frame to use to create a model matrix. This is an alternative to 'full' when the model matrix needs to be based on a data frame other than the data frame used for fitting the model.
`data`	data frame used as `"data"` attribute fot list elements returned only if the corresponding element of `L.` has a `NULL` data attribute
`debug`	(default `FALSE`) produce verbose information
`maxrows`	maximum number of rows of hypothesis matrix for which a full variance-covariance matrix is returned
`full`	if `TRUE`, the hypothesis matrix is the model matrix for `fit` such that the estimated coefficients are the predicted values for the fixed portion of the model. This is designed to allow the calculation of standard errors for models for which the `predict` method does not provide them.
`fixed`	normally if `L.` is a character string, it's treated as a regular expression; if `fixed` is `TRUE`, `L.` is interpreted literally, i.e., characters that have a special meaning in regular expressions are interpreted literally.
`invert`	if `L.` is a character string to be used as a regular expression, `invert == TRUE` causes the matches to be inverted so that coefficients that do not match will be selected.
`method`	`"svd"` (current default) or `"qr"` is the method used to find the full rank version of the hypothesis matrix. (`"svd"` has correctly identified the rank of a large hypothesis matrix where `"qr"` has failed.)
`df`	denominator degrees of freedom (overrides usual value).
`pars`	passed to `extract` for `"stanfit"` objects.
`tol.df`	tolerance for detecting reliable computation of degrees of freedom (default, `1e6`).
`tol.qr`	zero tolerance (default `1e-10`).
`..., optional`	to match generic, ignored.
`x`	a `"wald"` object.
`row.names`	optional row names for the resulting data frame.
`se`	multiplier (default 2) for standard errors in computing confidence limits.
`digits, round`	number of digits to the right of the decimal.
`sep`	separator character, for creating names, default is `""` (no separator).
`which`	which element(s) of a `"wald"` object to convert to a data frame.

Tests a general linear hypothesis for the linear fixed portion of a model. The hypothesis can be specified in a variety of ways such as a hypothesis matrix or a pattern that is used as a regular expression to be matched with the names of coefficients of the model. A number of tools are available to facilitate the generation of hypothesis matrices.

wald correctly handles hypotheses for stable regression splines generated by functions returned by gspline.

Usage:

wald(fit, L) where L is a hypothesis matrix

wald(fit, "pat") where "pat" is a regular expression (see regex) used to match names of coefficients of fixed effects. e.g. wald( fit, ":.*:") tests all second and higher order interactions.

wald(fit, c(2, 5, 6)) to test 2nd, 5th and 6th coefficients.

wald(fit, list(hyp1 = c(2, 5, 6), H2 = "pat")) for more than one hypothesis matrix.

To extend the wald function to a new class of objects, one needs to write a getFix method to extract estimated coefficients, their estimated covariance matrix, and the denominator degrees of freedom for each estimated coefficient.

An object of class wald.

Georges Monette

To extend to new models see getFix. To generate hypothesis matrices for general splines see gspline.

if (require(nlme)){
###
### Using wald to create and plot a data frame with predicted values
###
MathAchieve$Sector <- MathAchSchool[as.character(MathAchieve$School), "Sector"]
fit <- lme(MathAch ~ (SES+I(SES^2)) * Sex * Sector, MathAchieve, random = ~ 1|School)
summary(fit)
pred <- expand.grid( SES = seq(-2,2,.1), Sex = levels(MathAchieve$Sex),
Sector = levels(MathAchieve$Sector))
pred
w <- wald(fit, getX(fit, data=pred)) # attaches data to wald.object
                                    # so it can be included in data frame
w <- wald(fit, pred = pred)
w <- as.data.frame(w)
head(w)
if(require("latticeExtra")){
     xyplot(coef ~ SES | Sector, w, groups = Sex,
            auto.key = TRUE, type = 'l',
            fit = w$coef,
            upper = with(w,coef+2*se),
            lower = with(w,coef-2*se),
            subscript = TRUE) +
         glayer(panel.fit(...))
}

wald(fit, 'Sex')  # test overall effect of Sex
wald(fit, ':Sex') # but no evidence of interaction with ses
wald(fit, '\\^2') # nor of curvature

# but we continue for the sake of illustration

L <- Lform(fit, list(0, 1, 2*SES, 0, Sex == 'Male', (Sex == 'Male')*2*SES), MathAchieve)
head(L)
(ww <- wald (fit, L ))
wald.dd <- as.data.frame(ww, se = 2)
head( wald.dd )

if (require("lattice")){
  xyplot(coef + U2 + L2 ~ SES | Sex, wald.dd,
         main= 'Increase in predicted mathach per unit increase in ses')
}
}