coef.trim: Extract TRIM model coefficients.

In rtrim: Trends and Indices for Monitoring Data

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:

• 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.

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)

rtrim documentation built on June 22, 2024, 10:39 a.m.