coef.trim  R Documentation 
Extract TRIM model coefficients.
## 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: \ln\mu_{ij}=\alpha_i + \beta\times(j1)
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^{(j1)} = b\mu_{ij1}
, 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.
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.
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()
data(skylark)
z < trim(count ~ site + time, data=skylark, model=2, overdisp=TRUE)
coefficients(z)
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