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