model.select {PVAClone}

Model selection for 'pva' objects

Description

Likelihood ratio calculation and model selection for (hierarchical) 'pva' objects.

pva.llr is the workhorse behind model.select. pva.llr can also be used for profile likelihood calculations if called iteratively (no wrapper presently).

Usage

pva.llr(null, alt, pred)
model.select(null, alt, B = 10^4)
## S3 method for class 'pvaModelSelect'
print(x, ...)

Arguments

null

A fitted 'pva' object representing the Null Hypothesis.

alt

A fitted 'pva' object representing the Alternative Hypothesis (usually broader model).

B

Number of replicates to be generated from the latent variables.

pred

A matrix of replicates from the latent variables, e.g. as returned by generateLatent. When there are no missing values and both the model objects for the null and alternative hypotheses are without observation error, pred can be missing. The log observations are used when pred is missing, and any user supplied values for pred are used if provided.

x

A model selection object to be printed.

...

Additional argument for print method.

Details

These functions implement Ponciano et. al.'s (2009) data cloning likelihood ratio algorithm (DCLR) to compute likelihood ratios for comparing hierarchical (random effect) models. In the population growth models context, these models are (1) with observation error population growth models, and/or (2) population growth models with missing observations.

The functions can also compute likelihood ratios when both of the population growth models are fixed effect models, e.g. without observation error Gompertz model Vs. without observation error Ricker model. See examples below and in pva.

Value

pva.llr returns a single numeric value, the log likelihood ratio of the two models (logLik0 - logLik1).

model.select returns a modified data frame with log likelihood ratio and various information criteria metrics (delta AIC, BIC, AICc).

The print method gives fancy model names and a human readable interpretation of the numbers.

Author(s)

Khurram Nadeem and Peter Solymos

References

Ponciano, J. M. et al. 2009. Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning. Ecology 90, 356–362.

Nadeem, K., Lele S. R., 2012. Likelihood based population viability analysis in the presence of observation error. Oikos 121, 1656–1664.

See Also

pva

Examples

## Not run: 
data(redstart)
m1 <- pva(redstart, gompertz("none"), 2, n.iter=1000)
m2 <- pva(redstart, gompertz("poisson"), 2, n.iter=1000)
m3 <- pva(redstart, gompertz("normal"), 2, n.iter=1000)
p <- generateLatent(m2, n.chains=1, n.iter=10000)
pva.llr(m1, m2, p)
model.select(m1, m2)
model.select(m1, m3)
model.select(m2, m3)

m1x <- pva(redstart, ricker("none"), 2, n.iter=1000)
m2x <- pva(redstart, ricker("poisson"), 2, n.iter=1000)
m3x <- pva(redstart, ricker("normal"), 2, n.iter=1000)

model.select(m1, m1x)
model.select(m2, m2x)
model.select(m3, m3x)

## missing data situation
data(paurelia)
m1z <- pva(paurelia, ricker("none"), 2, n.iter=1000)
m2z <- pva(paurelia, ricker("poisson"), 2, n.iter=1000)
m3z <- pva(paurelia, ricker("normal"), 2, n.iter=1000)

#model.select(m1z, m2z) # not yet implemented
#model.select(m1z, m3z) # not yet implemented
model.select(m2z, m3z)

## Analysis of song sparrow data in Nadeem and Lele (2012)
## use about 100 clones to get MLE's repoted in the paper.
data(songsparrow)
m1z <- pva(songsparrow, 
    thetalogistic_D("normal",fixed=c(sigma2.d=0.66)), 
    n.clones=5, n.adapt=3000, n.iter=1000)
m2z <- pva(songsparrow, 
    thetalogistic_D("normal",fixed=c(theta=1, sigma2.d=0.66)), 
    n.clones=5, n.adapt=3000,n.iter=1000)
m3z <- pva(songsparrow, 
    thetalogistic_D("none",fixed=c(sigma2.d=0.66)), 
    n.clones=5, n.adapt=3000,n.iter=1000)
m4z <- pva(songsparrow, 
    thetalogistic_D("none",fixed=c(theta=1,sigma2.d=0.66)), 
    n.clones=5, n.adapt=3000,n.iter=1000)

model.select(m2z, m1z) 
model.select(m3z, m1z) 
model.select(m4z, m1z)

## profile likelihood
m <- pva(redstart, gompertz("normal"), 5, n.iter=5000)
p <- generateLatent(m, n.chains=1, n.iter=10000)
m1 <- pva(redstart, gompertz("normal", 
    fixed=c(sigma=0.4)), 5, n.iter=5000)
## etc for many sigma values
pva.llr(m1, m, p) # calculate log LR for each
## finally, fit smoother to points and plot

## End(Not run)