Enum_compare: Compare Expected Number of Species at ModelSites

In sustainablefarms/linking-data: OBSOLETE: Linking Data Project R Package

Description

Compare Expected Number of Species at ModelSites

Usage

Enum_compare(observed, predicted, predictedV)

Enum_coverage(observed, predicted, predictedV)

Arguments

observed	A list of the number of species observed for each ModelSite
predicted	A dataframe or matrix with each column the expected number of species detected from a single model. Each row is a ModelSite in the same order as observed.
predictedV	Same as predicted, but the variance of the number of species detected.

Details

Very similar to elpd_compare(). Assume each ModelSite with detection parameters are iid samples from a common distribution. In this regime the expected number of species for a ModelSite and the observed number of species, are both random variables.

For a correct model and given covariates for a ModelSite, the difference between the observed number of species and expected number of species is a random variable with mean 0, and fixed variance. For a ModelSite drawn from the common distribution, the mean is still 0, and the variance is a random variable. The variance of species numbers for a ModelSite drawn at random can be estimated from the fixed variance computed for many iid ModelSite covariate draws by averaging:

V[D] = E[D^2] - E[D]^2 = E[E[D^2|X]] - E[E[D|X]]^2 = E[E[D^2|X]] = E[E[(N - E[N|X])^2|X]] = E[E[N^2|X] - E[N|X]^2] = E[V[N|X]]

The variance of species numbers for a ModelSite drawn at random can also be estimated from many observed ModelSites by averaging:

V[D] = V[N - E[N|X]]

The mean difference can also be estimated from observations (and should be zero):

0 = E[D] = E[E[D|X]] ~ \frac{1}{m}∑_{i = 1}^m d_i

No bias correction for use of insample data is included.

Value

A matrix with a column for the aggregate (summed) difference of model sites between models, and the standard error of this difference (computed as the sample standard deviation of difference, multiplied by the square root of the number of ModelSites)

Functions

• Enum_coverage: The coverage of approximate 95% credence interval of each model.

Examples

inputdata <- readRDS("./private/data/clean/7_2_10_input_data.rds")
observed <- detectednumspec(inputdata$holdoutdata$yXobs[, inputdata$species], 
                            inputdata$holdoutdata$yXobs[, "ModelSiteID", drop = TRUE])
modelspecs <- readRDS("./tmpdata/7_3_00_modelspecs.rds")
filenames <- lapply(modelspecs, function(x) x$filename)
a <- vapply(filenames, file.exists, FUN.VALUE = FALSE)
fittedmods <- lapply(filenames, function(x) {
  fit <- readRDS(x)
  return(fit)})
prednumbers_l <- lapply(
  fittedmods, function(fit) {
    predsumspecies_newdata(fit,
                           inputdata$holdoutdata$Xocc,
                           inputdata$holdoutdata$yXobs,
                           ModelSiteVars = "ModelSiteID")
  })
predicted <- do.call(cbind, lapply(prednumbers_l, function(x) x["Esum_det", , drop = TRUE]))
predictedV <- do.call(cbind, lapply(prednumbers_l, function(x) x["Vsum_det", , drop = TRUE]))
Enum_compare(observed, predicted, predictedV)

sustainablefarms/linking-data documentation built on Oct. 28, 2020, 2:41 a.m.