# CIbeta: Confidence intervals for working (i.e., beta) parameters In momentuHMM: Maximum Likelihood Analysis of Animal Movement Behavior Using Multivariate Hidden Markov Models

## Description

Computes the standard errors and confidence intervals on the beta (i.e., working) scale of the data stream probability distribution parameters, as well as for the transition probabilities regression parameters. Working scale depends on the real (i.e., natural) scale of the parameters. For non-circular distributions or for circular distributions with `estAngleMean`=FALSE:

## Usage

 `1` ```CIbeta(m, alpha = 0.95) ```

## Arguments

 `m` A `momentuHMM` object `alpha` Significance level of the confidence intervals. Default: 0.95 (i.e. 95% CIs).

## Details

1) if both lower and upper bounds are finite then logit is the working scale; 2) if lower bound is finite and upper bound is infinite then log is the working scale.

For circular distributions with `estAngleMean`=TRUE and no constraints imposed by a design matrix (DM) or bounds (userBounds), then the working parameters are complex functions of both the angle mean and concentrations/sd natural parameters (in this case, it's probably best just to focus on the real parameter estimates!). However, if constraints are imposed by DM or userBounds on circular distribution parameters with `estAngleMean`=TRUE and `circularAngleMean`=FALSE:

1) if the natural bounds are (-pi,pi] then tangent is the working scale, otherwise if both lower and upper bounds are finite then logit is the working scale; 2) if lower bound is finite and upper bound is infinite then log is the working scale.

When circular-circular regression is specified using `circularAngleMean`, the working scale for the mean turning angle is not as easily interpretable, but the link function is atan2(sin(X)*B,1+cos(X)*B), where X are the angle covariates and B the angle coefficients. Under this formulation, the reference turning angle is 0 (i.e., movement in the same direction as the previous time step). In other words, the mean turning angle is zero when the coefficient(s) B=0.

## Value

A list of the following objects:

 `...` List(s) of estimates ('est'), standard errors ('se'), and confidence intervals ('lower', 'upper') for the working parameters of the data streams `beta` List of estimates ('est'), standard errors ('se'), and confidence intervals ('lower', 'upper') for the working parameters of the transition probabilities

## Examples

 ```1 2 3 4``` ```# m is a momentuHMM object (as returned by fitHMM), automatically loaded with the package m <- example\$m CIbeta(m) ```

momentuHMM documentation built on July 7, 2021, 9:06 a.m.