rtrim (version 2.1.1)

coef.trim: Extract TRIM model coefficients.

Description

Extract TRIM model coefficients.

Usage

# S3 method for 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.

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:

• Model 2: \(\ln\mu_{ij}=\alpha_i + \beta\times(j-1)\)

• Model 3: \(\ln\mu_{ij}=\alpha_i + \gamma_j\).

Here, \(\mu_{ij}\) is the estimated number of counts at site \(i\), time \(j\). The parameters \(\alpha_i\), \(\beta\) and \(\gamma_j\) 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

• Model 2: \(\mu_{ij}= a_ib^{(j-1)} = b\mu_{ij-1}\), where \(a_i=e^{\alpha_i}\) and \(b=e^\beta\).

• Model 3: \(\mu_{ij}=a_ic_j\), where \(a_i=e^{\alpha_i}\), \(c_1=1\) and \(c_j=e^{\gamma_j}\) for \(j>1\).

The parameters \(a_i\), \(b\) and \(c_j\) are referred to as coefficients in the multiplicative form.

Trend and deviation (Model 3 only)

The equation for Model 3

\(\ln\mu_{ij} = \alpha_i + \gamma_j\),

can also be written as an overall slope resulting from a linear regression of the \(\mu_{ij}\) 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

\(\ln\mu_{ij} = \alpha_i^* + \beta^*d_j + \gamma_j^*,\)

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

• The \(\alpha_i^*\) are the mean \(\ln\mu_{ij}\) per site

• The \(\gamma_j^*\) must sum to zero.

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

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

Details

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

See Also

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

Examples

# NOT RUN {
data(skylark)
z <- trim(count ~ site + time, data=skylark, model=2, overdisp=TRUE)
coefficients(z)
# }