Interactions with session effects

[howeer]

Good day,

We're trying to use AICc values to determine whether g0 and sigma vary among study areas, which we are modeling as different sessions. At the same time, we'd like to use the parameter and density estimates from models with session effects to investigate whether our study area-specific samples are adequate to estimate density to an acceptable level of precision from models that allow for individual heterogeneity. My questions are:

Is fitting a conditional likelihood model defined as g0~session, sigma~session equivalent to fitting the null model to data from each session? I.e. would parameter estimates be the same?

Similarly, will fitting the model g0~h2*session, sigma h2*session yield the same parameter estimates as fitting model g0~h2, sigma~h2 to data from each session?

Thanks,
Eric

[murray.efford]

[sorry I missed this before]

Is fitting a conditional likelihood model defined as g0~session, sigma~session equivalent to fitting the null model to data from each session? I.e. would parameter estimates be the same?

Similarly, will fitting the model g0~h2*session, sigma h2*session yield the same parameter estimates as fitting model g0~h2, sigma~h2 to data from each session?

Yes and yes: fitting a fully session-specific model is the same as fitting each session separately, but slower. I haven't checked the finite mixture example. You can verify for yourself as below.
Murray

Code: Select all

library(secr)
fit1 <- secr.fit(ovenCH, model = list(g0~session, sigma~session), CL = T, trace = F)
fit2 <- lapply(ovenCH, secr.fit, CL = T, trace = F)
derived(fit1)
$`2005`
     estimate SE.estimate       lcl      ucl       CVn       CVa       CVD
esa 15.883462          NA        NA       NA        NA        NA        NA
D    1.259171   0.3220943 0.7687577 2.062434 0.2236068 0.1242293 0.2557986

$`2006`
     estimate SE.estimate       lcl      ucl       CVn        CVa       CVD
esa 16.470601          NA        NA       NA        NA         NA        NA
D    1.335713   0.3140503 0.8477472 2.104554 0.2132007 0.09912596 0.2351181

$`2007`
     estimate SE.estimate       lcl      ucl       CVn        CVa      CVD
esa 17.424501          NA        NA       NA        NA         NA       NA
D    1.492152   0.3152559 0.9906821 2.247459 0.1961161 0.07858762 0.211276

$`2008`
     estimate SE.estimate       lcl     ucl       CVn       CVa      CVD
esa 11.981819          NA        NA      NA        NA        NA       NA
D    1.585736   0.4702198 0.8976814 2.80117 0.2294157 0.1878804 0.296531

$`2009`
      estimate SE.estimate       lcl      ucl  CVn        CVa       CVD
esa 18.2887590          NA        NA       NA   NA         NA        NA
D    0.8748543   0.2326004 0.5241761 1.460139 0.25 0.09049085 0.2658733

lapply(fit2, derived)
$`2005`
     estimate SE.estimate       lcl      ucl       CVn       CVa       CVD
esa 15.883579          NA        NA       NA        NA        NA        NA
D    1.259162   0.3220909 0.7687531 2.062416 0.2236068 0.1242278 0.2557979

$`2006`
     estimate SE.estimate       lcl      ucl       CVn        CVa       CVD
esa 16.470589          NA        NA       NA        NA         NA        NA
D    1.335714   0.3140488 0.8477499 2.104551 0.2132007 0.09912294 0.2351168

$`2007`
     estimate SE.estimate       lcl      ucl       CVn        CVa       CVD
esa 17.424483          NA        NA       NA        NA         NA        NA
D    1.492153   0.3152552 0.9906844 2.247458 0.1961161 0.07858575 0.2112753

$`2008`
     estimate SE.estimate       lcl      ucl       CVn       CVa       CVD
esa 11.981812          NA        NA       NA        NA        NA        NA
D    1.585737   0.4702211 0.8976808 2.801175 0.2294157 0.1878815 0.2965317

$`2009`
     estimate SE.estimate       lcl      ucl  CVn        CVa       CVD
esa 18.288744          NA        NA       NA   NA         NA        NA
D    0.874855   0.2326041 0.5241726 1.460151 0.25 0.09050274 0.2658773