Description Usage Arguments Value Details Additive versus multiplicative representation Trend and deviation (Model 3 only) See Also Examples
Extract TRIM model coefficients.
1 2 | ## S3 method for class 'trim'
coef(object, representation = c("standard", "trend", "deviations"), ...)
|
object |
TRIM output structure (i.e., output of a call to |
representation |
|
... |
currently unused |
A data.frame
containing coefficients and their standard errors,
both in additive and multiplicative form.
Extract the site, growth or time effect parameters computed with
trim
.
In the simplest cases (no covariates, no change points), the trim Model 2 and Model 3 can be summarized as follows:
Model 2: \lnμ_{ij}=α_i + β\times(j-1)
Model 3: \lnμ_{ij}=α_i + γ_j.
Here, μ_{ij} is the estimated number of counts at site i, time j. The parameters α_i, β and γ_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: μ_{ij}= a_ib^{(j-1)} = bμ_{ij-1}, where a_i=e^{α_i} and b=e^β.
Model 3: μ_{ij}=a_ic_j, where a_i=e^{α_i}, c_1=1 and c_j=e^{γ_j} for j>1.
The parameters a_i, b and c_j are referred to as coefficients in the multiplicative form.
The equation for Model 3
\lnμ_{ij} = α_i + γ_j,
can also be written as an overall slope resulting from a linear regression of the μ_{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
\lnμ_{ij} = α_i^* + β^*d_j + γ_j^*,
where d_j equals j minus the mean over all j (i.e. if j=1,2,…,J then d_j = j-(J+1)/2). It is not hard to show that
The α_i^* are the mean \lnμ_{ij} per site
The γ_j^* must sum to zero.
The coefficients α_i^* and γ_j^* are obtained by
setting representation="deviations"
. If representation="trend"
,
the overall trend parameters β^* and α^* from the overall
slope defined by α^* + β^*d_j is returned.
Finally, note that both the overall slope and the deviations can be written in multiplicative form as well.
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()
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