betaContinuous {cNORM}

Continuous Norming with Beta-Binomial Distribution (experimental)

Description

This function models the alpha ('a') and beta ('b') parameters of the beta-binomial distribution across groups using polynomial regression. It then calculates the distribution's properties (cumulative probabilities, density, percentiles, and z-scores) for these modeled parameters. The modeling of 'a' and 'b' allows for the investigation of how these parameters vary with a continuous group variable, allowing for continuous norming.

Usage

betaContinuous(param, powerA = Inf, powerB = Inf)

Arguments

param

A data frame containing the columns 'a', 'b', 'group', and 'n'. Each row should represent a distinct group with its corresponding beta-binomial parameters and the group identifier. These parameters can be obtained with the 'betaByGroup' function.

powerA

The degree of the polynomial used to model the 'a' parameter across groups. Please choose powerA \leq k with k being the number of groups.

powerB

The degree of the polynomial used to model the 'b' parameter across groups. Please choose powerB \leq k with k being the number of groups.

Details

The function first fits polynomial regression models for 'a' and 'b' against a continuous group variable, allowing for non-linear trends in how the shape parameters of the beta-binomial distribution change with the group. It then predicts 'a' and 'b' for each group, using these predicted values to calculate the beta-binomial distribution's properties for each group. This approach facilitates understanding the variability and dynamics of the distribution across different conditions or groups.

Value

A list containing several components: 'manifestParameters' with the input parameters, 'powerA' and 'powerB' showing the polynomial degrees used, 'modA' and 'modB' with the polynomial regression models for 'a' and 'b' parameters.

Examples

param <- data.frame(a = c(1,2,3), b = c(2,3,4), group = c(1,2,3), n = c(30,30,30))
powerA <- 2
powerB <- 2
betaContinuous(param, powerA, powerB)