# relativity_template: Template to input Covariate Relativities In SynthETIC: Synthetic Experience Tracking Insurance Claims

 relativity_template R Documentation

## 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)


### 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.

### 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.

### 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
)

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"
)



SynthETIC documentation built on May 29, 2024, 8:47 a.m.