spaMM: predict – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

predict

Prediction from a model fit

Description

The following functions can be used to compute point predictions and/or various measures of uncertainty associated to such predictions. predict can be used for prediction of the response variable by its expected value obtained as (the inverse link transformation of) the linear predictor (η) and more generally for terms of the form X_nβ+Z_nLv, for new design matrices X_n and Z_n. Various components of prediction variances and predictions intervals can also be computed using predict. The get_... functions are convenient extractors for such components. get_predCov_var_fix extracts a block of a prediction covariance matrix. It was conceived for the specific purpose of computing the spatial prediction covariances between two “new” sets of geographic locations, without computing the full covariance matrix for both the new locations and the original (fitted) locations. When one of the two sets of new locations is fixed while the other varies, some expensive computations can be performed once for all sets of new locations, and be provided as the fix_X_ZAC.object argument. The preprocess_fix_corr extractor is designed to compute this argument.

Usage

## S3 method for class 'HLfit'
predict(object, newdata = newX, newX = NULL, re.form = NULL,
                        variances=list(), binding = FALSE, intervals = NULL,
                        level = 0.95, blockSize = 2000L, type = "response", 
                        verbose=c(showpbar=eval(spaMM.getOption("barstyle"))), 
                        control=list(), ...)
get_predCov_var_fix(object, newdata = NULL, fix_X_ZAC.object, fixdata, re.form = NULL,
                    variances=list(disp=TRUE,residVar=FALSE,cov=FALSE), 
                    control=list(),  ...)    
preprocess_fix_corr(object, fixdata, re.form = NULL,
                   variances=list(residVar=FALSE, cov=FALSE), control=list())
get_fixefVar(...)
get_predVar(..., variances=list(), which="predVar")
get_residVar(...)
get_respVar(...)
get_intervals(..., intervals="predVar")

Arguments

`object`	The return object of fitting functions `HLfit,corrHLfit,HLCor`... returning an object inheriting from `HLfit` class.
`newdata`	Either NULL, a matrix or data frame, or a numeric vector. If `NULL`, the original data are reused. Otherwise, all variables required to evaluate model formulas must be included. Which variables are required may depend on other arguments: see “prediction with given phi's” example, also illustrating the syntax when formulas include an offset. If `newdata` is a numeric vector, its names (if any) are ignored. This makes it easier to use `predict` as an objective function for an optimization procedure such as `optim`, which calls the objective function on unnamed vectors. However, one must make sure that the order of elements in the vector is the order of first occurrence of the variables in the model formula. This order can be checked in the error message returned when calling `predict` on a `newX` vector of clearly wrong size, e.g. `predict(<object>,newdata=numeric(0))`.
`newX`	equivalent to newdata, available for back-compatibility
`re.form`	formula for random effects to include. By default, it is NULL, in which case all random effects are included. If it is NA, no random effect is included. If it is a formula, only the random effects it contains are retained. The other variance components are removed from both point prediction and `variances` calculations. If you want to retain only the spatial effects in the point prediction, but all variances, either use re.form and add missing variances (on linear predictor scale) manually, or ignore this argument and see Details and Examples for different ways of controlling variances.
`variances`	A list whose elements control the computation of different estimated variances. `predict` can return four components of prediction variance: `fixefVar`, `predVar`, `residVar` and `respVar`. They are all returned as attributes of the point predictions. In particular, `variances=list(predVar=TRUE)` is suitable for uncertainty in point prediction, distinguished from the response variance given by `list(respVar=TRUE)`. See the `predVar` help page for further explanations and other options.
`intervals`	NULL or character string or vector of strings. Provides prediction intervals with nominal level `level`, deduced from the given prediction variance term, e.g. `intervals="predVar"`. Currently only intervals from `fixefVar` and `predVar` (and for LMMs `respVar` including the residual variance) may have a probabilistic meaning. Intervals returned in other cases are (currently) meaningless.
`which`	any of `"predVar"`,`"respVar"`,`"residVar"`, `"fixefVar"`, `"intervals"`, or `"naive"`
`level`	Coverage of the intervals.
`binding`	If `binding` is a character string, the predicted values are bound with the `newdata` and the result is returned as a data frame. The predicted values column name is the given `binding`, or a name based on it if the `newdata` already include a variable with this name. If `binding` is `FALSE`, The predicted values are returned as a one-column matrix and the data frame used for prediction is returned as an attribute (unless it was `NULL`). If `binding` is `NA`, a vector is returned, without the previous attributes.
`fixdata`	A data frame describing reference data whose covariances with variable `newdata` may be requested.
`fix_X_ZAC.object`	The return value of calling `preprocess_fix_corr` (see trivial Example). This is a more efficient way of providing information about the `fixdata` for repeated calls to `get_predCov_var_fix` with variable `newdata`.
`blockSize`	Mainly for development purposes. For original or new data with many rows, it may be more efficient to split these data in small blocks, and this gives the maximum number or rows of the blocks. However, this will be ignored if a prediction covariance matrix is requested.
`type`	character string; The returned point prediction is on the response scale if `type="response"` (the default; for binomial response, a frequency 0<.<1). It is on the linear predictor scale if `type="link"`.
`control`	A list; a warning will direct you to relevant usage when needed.
`verbose`	A vector of booleans; it single currently used element is `"showpbar"`, which controls whether to show a progress bar in certain prediction variance computations.
`...`	further arguments passed to or from other methods. For the `get_`... functions, they are passed to `predict`.

Details

See the predVar help page for information about the different concepts of prediction variances handled by spaMM (uncertainty of point prediction vs. of response) and about options controlling their computation.

If newdata is NULL, predict returns the fitted responses, including random effects, from the object. Otherwise it computes new predictions including random effects as far as possible. For spatial random effects it constructs a correlation matrix C between new locations and locations in the original fit. Then it infers the random effects in the new locations as C (L')^{-1} v (see spaMM for notation). For non-spatial random effects, it checks whether any group (i.e., level of a random effect) in the new data was represented in the original data, and it adds the inferred random effect for this group to the prediction for individuals in this group.

In the point prediction of the linear predictor, the unconditional expected value of u is assigned to the realizations of u for unobserved levels of non-spatial random effects (it is zero in GLMMs but not for non-gaussian random effects), and the inferred value of u is assigned in all other cases. Corresponding values of v are then deduced. This computation yields the classical “BLUP” or empirical Bayes predictor in LMMs, but otherwise it may yield less well characterized predictors, where “unconditional” v may not be its expected value when the rand.family link is not identity.

Intervals computations use the relevant variance estimates plugged in a Gaussian approximation, except for the simple linear model where it uses Student's t distribution.

Value

See Details in Tpoisson for questions specific to truncated distributions.

For predict, a matrix or data frame (according to the binding argument), with optional attributes frame, intervals, predVar, fixefVar, residVar, and/or respVar, the last four holding one or more variance vector or covariance matrices. The further attribute fittedName contains the binding name, if any.

The get_... extractor functions call predict and extract from its result the attribute implied by the name of the extractor. By default, get_intervals will return prediction intervals using predVar. get_predVar with non-default which argument has the same effect as the get_... function whose name is implied by which.

Examples

data("blackcap")
fitobject <- fitme(migStatus ~ 1 + Matern(1|longitude+latitude),data=blackcap,
                       fixed=list(nu=4,rho=0.4,phi=0.05))
predict(fitobject)

#### multiple controls of prediction variances
## (1) fit with an additional random effect
grouped <- cbind(blackcap,grp=c(rep(1,7),rep(2,7))) 
fitobject <- fitme(migStatus ~ 1 +  (1|grp) +Matern(1|longitude+latitude),
                       data=grouped,  fixed=list(nu=4,rho=0.4,phi=0.05))

## (2) re.form usage to remove a random effect from point prediction and variances: 
predict(fitobject,re.form= ~ 1 +  Matern(1|longitude+latitude))

## (3) comparison of covariance matrices for two types of new data
moregroups <- grouped[1:5,]
rownames(moregroups) <- paste0("newloc",1:5)
moregroups$grp <- rep(3,5) ## all new data belong to an unobserved third group 
cov1 <- get_predVar(fitobject,newdata=moregroups,
                     variances=list(linPred=TRUE,cov=TRUE))
moregroups$grp <- 3:7 ## all new data belong to distinct unobserved groups
cov2 <- get_predVar(fitobject,newdata=moregroups,
                     variances=list(linPred=TRUE,cov=TRUE))
cov1-cov2 ## the expected off-diagonal covariance due to the common group in the first fit.

## Not run: 
#### Other extractors:
fix_X_ZAC.object <- preprocess_fix_corr(fitobject,fixdata=blackcap)
# ... for use in multiple calls to get_predCov_var_fix():
get_predCov_var_fix(fitobject,newdata=blackcap[14,],fix_X_ZAC.object=fix_X_ZAC.object)

#### Prediction with distinct given phi's in different locations, 
#   as specified by a resid.model:
varphi <- cbind(blackcap,logphi=runif(14))
vphifit <- fitme(migStatus ~ 1 + Matern(1|longitude+latitude), 
                     resid.model = list(formula=~0+offset(logphi)),
                     data=varphi,  fixed=list(nu=4,rho=0.4))

# For respVar computation (i.e., response variance, often called prediction variance), 
#   one then also needs to provide the variables used in 'resid.model', here 'logphi':
get_respVar(vphifit,newdata=data.frame(latitude=1,longitude=1,logphi=1))

# For default 'predVar' computation (i.e., uncertainty in point prediction), 
#   this is not needed: 
get_predVar(vphifit,newdata=data.frame(latitude=1,longitude=1))                     

#### point predictions and variances with new X and Z
if(requireNamespace("rsae", quietly = TRUE)) {
  data("landsat", package = "rsae")
  fitobject <- fitme(HACorn ~ PixelsCorn + PixelsSoybeans + (1|CountyName),
                     data=landsat[-33,])
  newXandZ <- unique(data.frame(PixelsCorn=landsat$MeanPixelsCorn,
                                PixelsSoybeans=landsat$MeanPixelsSoybeans,
                                CountyName=landsat$CountyName))
  predict(fitobject,newdata=newXandZ,variances = list(predVar=TRUE))
  get_predVar(fitobject,newdata=newXandZ,variances = list(predVar=TRUE))
}


## End(Not run)

spaMM

Mixed-Effect Models, with or without Spatial Random Effects

v3.10.0

CeCILL-2

Authors

François Rousset [aut, cre, cph] (<https://orcid.org/0000-0003-4670-0371>), Jean-Baptiste Ferdy [aut, cph], Alexandre Courtiol [aut] (<https://orcid.org/0000-0003-0637-2959>), GSL authors [ctb] (src/gsl_bessel.*)

Initial release

2022-02-06