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Compute Latent Variables

Source: R/intData_utils.r
get_latent_var.Rd

Obtain the latent variables inherent to the macrodata.

Usage

get_latent_var(
  microdata,
  macrodata,
  agrby,
  agrlevels,
  Seq = c("AllLb_AllUb", "AllCen_AllRng", "LbUb_VarbyVar", "CenRng_VarbyVar")
)

Arguments

microdata

A matrix containing the microdata.

macrodata

A data frame, matrix or intData object containing the macrodata/interval data.

agrby

A factor used to specify the grouping of the microdata.

agrlevels

The categories/levels on which the microdata was aggregated.

Seq

Format of macrodata if it is a data frame or matrix. Available options are:

  • "AllLb_AllUb": All lower bounds followed by all upper bounds, in the same variable order.

  • "AllCen_AllRng": All Centers followed by all Ranges, in the same variable order.

  • "LbUb_VarbyVar": Lower bounds followed by upper bounds, variable by variable.

  • "CenRng_VarbyVar": Centers followed by Ranges, variable by variable.

Value

A matrix with the same size as the microdata.

Details

The latent variables, \(U_{j}\), are defined according to the following model:

Let \(X_j=(C_j,R_j)^\top=\left[C_j-\dfrac{R_j}{2}, C_j+\dfrac{R_j}{2}\right]\) represent the macrodata and $$V_{j}=C_j+U_{j}\dfrac{R_j}{2},\quad j=1,\dots,p,$$ the microdata with \(U_{j}\) being random variables with support on \([-1,1]\), uncorrelated with \((C_j,R_j)\).

References

Oliveira, M.R., Azeitona, M., Pacheco, A., Valadas, R.. Association measures for interval variables. Advances in Data Analysis and Classification 16, 491–520 (2022). doi:10.1007/s11634-021-00445-8

Examples

data(creditcard)
CreditCard_min_max <- creditcard$min_max
CreditCard_microdata <- creditcard$microdata

# Define grouping variable for microdata aggregation
credit_agrby <- paste(CreditCard_microdata$Name, CreditCard_microdata$Month, sep = "_")

# Obtain latent variables inherent to the macrodata (standardized to [-1,1])
credit_card_U <- get_latent_var(microdata = CreditCard_microdata[,3:7], 
                                macrodata = CreditCard_min_max, 
                                agrby = credit_agrby, 
                                agrlevels = row.names(CreditCard_min_max), 
                                Seq = "LbUb_VarbyVar")