coef.trim {rtrim}R Documentation

Extract TRIM model coefficients.

Description

Extract TRIM model coefficients.

Usage

## S3 method for class 'trim'
coef(object, representation = c("standard", "trend", "deviations"), ...)

Arguments

object

TRIM output structure (i.e., output of a call to trim)

representation

[character] Choose the coefficient representation. Options "trend" and "deviations" are for model 3 only.

...

currently unused

Value

A data.frame containing coefficients and their standard errors, both in additive and multiplicative form.

Details

Extract the site, growth or time effect parameters computed with trim.

Additive versus multiplicative representation

In the simplest cases (no covariates, no change points), the trim Model 2 and Model 3 can be summarized as follows:

Here, μij\mu_{ij} is the estimated number of counts at site ii, time jj. The parameters αi\alpha_i, β\beta and γj\gamma_j are refererred to as coefficients in the additive representation. By exponentiating both sides of the above equations, alternative representations can be written down. Explicitly, one can show that

The parameters aia_i, bb and cjc_j are referred to as coefficients in the multiplicative form.

Trend and deviation (Model 3 only)

The equation for Model 3

lnμij=αi+γj\ln\mu_{ij} = \alpha_i + \gamma_j,

can also be written as an overall slope resulting from a linear regression of the μij\mu_{ij} over time, plus site- and time effects that record deviations from this overall slope. In such a reparametrisation the previous equation can be written as

lnμij=αi+βdj+γj,\ln\mu_{ij} = \alpha_i^* + \beta^*d_j + \gamma_j^*,

where djd_j equals jj minus the mean over all jj (i.e. if j=1,2,,Jj=1,2,\ldots,J then dj=j(J+1)/2d_j = j-(J+1)/2). It is not hard to show that

The coefficients αi\alpha_i^* and γj\gamma_j^* are obtained by setting representation="deviations". If representation="trend", the overall trend parameters β\beta^* and α\alpha^* from the overall slope defined by α+βdj\alpha^* + \beta^*d_j is returned.

Finally, note that both the overall slope and the deviations can be written in multiplicative form as well.

See Also

Other analyses: confint.trim(), gof(), index(), now_what(), overall(), overdispersion(), plot.trim.index(), plot.trim.overall(), plot.trim.smooth(), results(), serial_correlation(), summary.trim(), totals(), trendlines(), trim(), vcov.trim(), wald()

Examples

data(skylark)
z <- trim(count ~ site + time, data=skylark, model=2, overdisp=TRUE)
coefficients(z)

[Package rtrim version 2.3.0 Index]