Score Test for SECR Models

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Description

Compute score tests comparing a fitted model and a more general alternative model.

Usage

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score.test(secr, ..., betaindex = NULL, trace = FALSE, ncores = 1, .relStep = 0.001,
    minAbsPar = 0.1)

score.table(object, ..., sort = TRUE, dmax = 10)

Arguments

secr

fitted secr model

...

one or more alternative models OR a fitted secr model

trace

logical. If TRUE then output one-line summary at each evaluation of the likelihood

ncores

integer number of cores available for parallel processing

.relStep

see fdHess

minAbsPar

see fdHess

betaindex

vector of indices mapping fitted values to parameters in the alternative model

object

score.test object or list of such objects

sort

logical for whether output rows should be in descending order of AICc

dmax

threshold of dAICc for inclusion in model set

Details

Score tests allow fast model selection (e.g. Catchpole & Morgan 1996). Only the simpler model need be fitted. This implementation uses the observed information matrix, which may sometimes mislead (Morgan et al. 2007). The gradient and second derivative of the likelihood function are evaluated numerically at the point in the parameter space of the second model corresponding to the fit of the first model. This operation uses the function fdHess of the nlme package; the likelihood must be evaluated several times, but many fewer times than would be needed to fit the model. The score statistic is an approximation to the likelihood ratio; this allows the difference in AIC to be estimated.

Covariates are inferred from components of the reference model secr. If the new models require additional covariates these may usually be added to the respective component of secr.

Mapping of parameters between the fitted and alternative models sometimes requires user intervention via the betaindex argument. For example betaindex = c(1,2,4) is the correct mapping when comparing the null model (D~1, g0~1, sigma~1) to one with a behavioural effect on g0 (D~1, g0~b, sigma~1).

The arguments .relStep and minAbsPar control the numerical gradient calculation and are passed directly to fdHess. More investigation is needed to determine optimal settings.

score.table summarises one or more score tests in the form of a model comparison table. The ... argument here allows the inclusion of additional score test objects (note the meaning differs from score.test). Approximate AICc values are used to compute relative AIC model weights for all models within dmax AICc units of the best model.

Multiple cores provide some speed improvment in score.test when comparing more than two models.

Value

An object of class ‘score.test’ that inherits from ‘htest’, a list with components

statistic

the value the chi-squared test statistic (score statistic)

parameter

degrees of freedom of the approximate chi-squared distribution of the test statistic (difference in number of parameters H0, H1)

p.value

probability of test statistic assuming chi-square distribution

method

a character string indicating the type of test performed

data.name

character string with null hypothesis, alternative hypothesis and arguments to function call from fit of H0

H0

simpler model

np0

number of parameters in simpler model

H1

alternative model

H1.beta

coefficients of alternative model

AIC

Akaike's information criterion, approximated from score statistic

AICc

AIC with small-sample adjustment of Hurvich & Tsai 1989

If ... defines several alternative models then a list of score.test objects is returned.

The output from score.table is a dataframe with one row per model, including the reference model.

Note

This implementation is experimental. The AIC values, and values derived from them, are approximations that may differ considerably from AIC values obtained by fitting and comparing the respective models. Use of the observed information matrix may not be optimal.

References

Catchpole, E. A. and Morgan, B. J. T. (1996) Model selection of ring-recovery models using score tests. Biometrics 52, 664–672.

Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples. Biometrika 76, 297–307.

McCrea, R. S. and Morgan, B. J. T. (2011) Multistate mark-recapture model selection using score tests. Biometrics 67, 234–241.

Morgan, B. J. T., Palmer, K. J. and Ridout, M. S. (2007) Negative score test statistic. American statistician 61, 285–288.

See Also

AIC, LR.test

Examples

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## Not run: 
    AIC (secrdemo.0, secrdemo.b)
    st <- score.test (secrdemo.0, g0 ~ b)
    st
    score.table(st)

    ## adding a time covariate to separate occasions (1,2) from (3,4,5)
    secrdemo.0$timecov <- data.frame(t2 = factor(c(1,1,2,2,2)))
    st2 <- score.test (secrdemo.0, g0 ~ t2)
    score.table(st,st2)

## End(Not run)

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