spaMM (version 4.7.0)

anova: ANOVA tables (and likelihood ratio tests).

Description

The anova method for fit objects from spaMM has two uses: if a single fit object is provided, ANOVA tables may be returned, with specific procedures for univariate-response LMs, GLMs and LMMs (see Details). Alternatively, if a second fit object is provided (object2 argument), anova performs as an alias for LRT.

Usage

# S3 method for HLfit
anova(object, object2, type = "2", method="", ...)

Value

The return format is that of the function called (lmerTest::anova for LMMs) or emulated (for LMs or GLMs). For GLMs, by default no test is reported, as has been the default for anova.glm before R 4.4.0.

Arguments

object

Fit object returned by a spaMM fitting function.

object2

Optional second model fit to be compared to the first (their order does not matter, except in non-standard cases where the second model is taken as the null one and a message is issued).

type

ANOVA type for LMMs, as interpreted by lmerTest. Note that the default (single-term deletion ANOVA) differs from that of lmerTest.

method

Only non-default value is "t.Chisq" which forces evaluation of a table of chi-squared tests for each fixed-effect term, using the classical “Wald” test (see Details). Further methods are available through the ... for specific classes of models.

...

Further arguments, passed to spaMM_boot (e.g., for parallelization) in the case of LRTs (i.e., when object2 is provided). For ANOVA tables, arguments of functions anova.lm anova.glm, and as_LMLT, respectively for LMs, GLMs and LMMs, may be handled (e.g. the test argument for anova.glm).

Details

The ANOVA-table functionality has been included in spaMM mainly to provide access to F tests (including, for LMMs, the “Satterthwaite method” as developed by Fai and Cornelius, 1996), using pre-existing procedures as template or backend for expediency and familiarity:

1. ANOVA tables for LMs and GLMs have been conceived to replicate the functionality, output format and details of base R anova, and therefore replicate some of their limitations, e.g., they only perform sequential analysis (“type 1”) in the same way as anova.lm and anova.glm. However, a difference occurs for Gamma GLMs, because the dispersion estimates for Gamma GLMs differ between stats::glm and spaMM fits (see Details in method). Therefore, F tests and Mallows' Cp differ too; results from spaMM REML fits being closer than ML fits to those from glm() fits;
   

2. For LMMs, ANOVA tables are provided by interfacing lmerTest::anova (with non-default type). This procedure should handle all types of LMMs that can be fitted by spaMM; yet, the displayed information should be inspected to check that some fitted random-effect parameters are not ignored when computing information for the Satterthwaite method.

3. For fitted models that do not lay within previous categories, such as GLMMs, models with a residual-dispersion submodel, and multivariate-response models, a table of tests for single-term deletions using the classical “Wald” chi-squared test based on coefficient values and their conditional standard error estimates will be returned. LRTs (moreover, with bootstrap correction) are more reliable than such tests and, as calling them requires a second model to be explicitly specified, they may also help users thinking about the hypothesis they are testing.

References

Fai AH, Cornelius PL (1996). Approximate F-tests of multiple degree of freedom hypotheses in generalised least squares analyses of unbalanced split-plot experiments. Journal of Statistical Computation and Simulation, 54(4), 363-378. tools:::Rd_expr_doi("10.1080/00949659608811740")

See Also

LRT,
as_LMLT for the interface to lmerTest::anova,
and summary.HLfit(.,details=list(<true|"Wald">)) for reporting the p-value for each t-statistic in the summary table for fixed effects, either by Student's t distribution, or by the approximation of t^2 distribution by the Chi-squared distribution (“Wald's test”).

Examples

data("wafers")
## Gamma GLMM with log link
m1 <- HLfit(y ~X1+X2+X1*X3+X2*X3+I(X2^2)+(1|batch),family=Gamma(log),
          resid.model = ~ X3+I(X3^2) ,data=wafers,method="ML")
m2 <- update(m1,formula.= ~ . -I(X2^2))
#
anova(m1,m2) # LRT

## 'anova' (Wald chi-squared tests...) for GLMM or model with a 'resid.model'
anova(m1) 

## ANOVA table for GLM
# Gamma example, from McCullagh & Nelder (1989, pp. 300-2), as in 'glm' doc:
clotting <- data.frame(
    u = c(5,10,15,20,30,40,60,80,100),
    lot1 = c(118,58,42,35,27,25,21,19,18),
    lot2 = c(69,35,26,21,18,16,13,12,12))
spglm <- fitme(lot1 ~ log(u), data = clotting, family = Gamma, method="REML")
anova(spglm, test = "F") 
anova(spglm, test = "Cp") 
anova(spglm, test = "Chisq")
anova(spglm, test = "Rao") 

## ANOVA table for LMM
if(requireNamespace("lmerTest", quietly=TRUE)) {
  lmmfit <- fitme(y ~X1+X2+X1*X3+X2*X3+I(X2^2)+(1|batch),data=wafers)
  print(anova(lmmfit)) # => Satterthwaite method, here giving p-values 
                       #   quite close to traditional t-tests given by:
  summary(lmmfit, details=list(p_value=TRUE))
}