relativity_template function

Template to input Covariate Relativities

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.

relativity_template(factors)

Arguments

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

Returns

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 .

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"
)