SynthETIC (version 1.1.0)

relativity_template: Template to input Covariate Relativities

Description

Constructs a template for the covariate relativities based on the inputed covariates. Note that only non-zero relativities and one cross-factor relativity is needed for each factor pair.

Usage

relativity_template(factors)

Value

Returns a dataframe object, with five columns:

factor_i	Factor i.
factor_j	Factor j.
level_ik	Level within Factor i.
level_jl	Level within Factor j.
relativity	Relativity between level_ik and level_jl, defaults to NA.

Arguments

factors

named list of vectors, containing the name of the covariates and associated factors in vector form.

Details

Suppose that there are \(m\) covariates labelled \(c_i\), \(i=1,...,m\), and that covariate \(c_i\) can assume one and only one of \(n_i\) values, \(x_{ik}\), \(k=1,...,n_i\). The total number of available covariate values is \(n = \sum_{i=1}^m n_o\).

Now set up an \(n \times n\) matrix \(F\), consisting of sub-matrices \(F_{ij}\), \(i,j = 1, ... ,m\) of dimension \(n_i \times n_j\). The diagonal blocks \(F_{ii}\) will quantify first-order relativities on claims attributes, and the off-diagonal blocks \(F_{ij}\), \(j \neq i\) will quantify second-order effects. Let \(f_{ij,kl}\) denote the \((k, l)\) element of \(F_{ij}\). This element operates as a multiplier of the claim attribute when covariates \(c_i\) and \(c_j\) take values \(x_{ik}\) and \(x_jl\) respectively. Since \(c_i\) can assume only one of the values \(x_ik\), \(f_{ii, kl} = 0\) for \(k \neq l\), and so \(F_{ii}\) is diagonal for all \(i=1, ..., m\). Moreover, \(f_{ij,kl} = f_{ji,lk}\), so that \(F\) is symmetric and \(f_{ij,kl} > 0\).

Examples

factors <- list(
    "Legal Representation" = c("Y", "N"),
    "Injury Severity" = as.character(1:6),
    "Age of Claimant" = c("0-15", "15-30", "30-50", "50-65", "over 65")
)

relativity_freq <- relativity_template(factors)
relativity_sev <- relativity_template(factors)

# Default Values
relativity_freq$relativity <- c(
    1, 1,
    0.95, 1, 1, 1, 1, 1,
    0.05, 0, 0, 0, 0, 0,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    0.53, 0.3, 0.1, 0.05, 0.01, 0.01,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    0.183, 0.192, 0.274, 0.18, 0.171
)

relativity_sev$relativity <- c(
    2, 1,
    1, 1, 1, 1, 1, 1,
    1, 1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    0.6, 1.2, 2.5, 5, 8, 0.4,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 1, 1,
    1, 1, 1, 0.97, 0.95,
    1, 1, 1, 0.95, 0.9,
    1, 1, 1, 1, 1,
    1.25, 1.15, 1, 0.85, 0.7
)

head(relativity_freq)
head(relativity_sev)

test_covariates_obj <- covariates(factors)
test_covariates_obj <- set.covariates_relativity(
    covariates = test_covariates_obj,
    relativity = relativity_freq,
    freq_sev = "freq"
)
test_covariates_obj <- set.covariates_relativity(
    covariates = test_covariates_obj,
    relativity = relativity_sev,
    freq_sev = "sev"
)