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Compute Latent Variables Parameters

Source: R/intData_utils.r
get_latent_param.Rd

Obtain the parameters of the latent variables inherent to the macrodata.

Usage

get_latent_param(
  LatentCase = c("U_id_symmetric", "U_id", "General"),
  LatentDist = c("Unif", "Triang", "TNorm", "InvTri", "Beta", "KDE", "Degenerated"),
  TriangParam = 0,
  BetaParam.a = 1,
  BetaParam.b = 1,
  Umicro = NULL,
  p = NULL,
  estimate.DistParam = FALSE
)

Arguments

LatentCase

A string specifying which of the three scenarios applies to the latent variables:

  • "U_id_symmetric": The case where the latent variables are identically distributed and symmetric.

  • "U_id": The case where the latent variables are identically distributed.

  • "General": The case where the latent variables do not have any nice properties.

Defaults to "U_id_symmetric".

LatentDist

A string or vector of strings specifying the distribution(s) of the latent variables. If the variables are identically distributed it can be one of ("Unif", "Triang", "TNorm", "InvTri", "Beta", "KDE", "Degenerated"), if not a vector must be provided with the distribution for each variable. The default is "Unif" if LatentCase="U_id_symmetric" or if Umicro is not provided, and "KDE" if LatentCase="General".

TriangParam

Mode of the triangular distribution. If the latent variables are identically distributed, it is only necessary to provide a number, if not a vector is needed. The default is 0.

BetaParam.a

Parameter alpha of the Beta distribution. If the latent variables are identically distributed, it is only necessary to provide a number, if not a vector is needed. The default is 1.

BetaParam.b

Parameter beta of the Beta distribution. If the latent variables are identically distributed, it is only necessary to provide a number, if not a vector is needed. The default is 1.

Umicro

Latent microdata observations. Needed if estimate.DistParam is TRUE or LatentDist is "KDE".

p

Number of variables.

estimate.DistParam

Logical parameter indicating if estimation of the parameters of the latent distributions should be performed. Can only be set to TRUE if LatentCase="General". The default is FALSE.

Value

A list composed by:

LatentParam

A list with the parameters of the latent variables distribution.

TriangParam

The mode of the triangular distribution.

BetaParam.a

The alpha parameter of the Beta distribution.

BetaParam.b

The beta parameter of the Beta distribution.

LatentCase

The case of the latent variables.

LatentDist

The distribution of the latent variables.

Details

The parameters of the latent variables inherent to the macrodata are defined according to the LatentCase:

  • "U_id_symmetric": The latent variables are identically distributed and symmetric, so its parameters are:

    • \(\delta=\mathbb{E}(U^2)/4\)

  • "U_id": The latent variables are identically distributed, so its parameters are:

    • \(\delta=\mathbb{E}(U^2)/4\)

    • \(\mathbb{E}(U)\)

  • "General": The latent variables do not have any nice properties, so its parameters are:

    • \([\boldsymbol{\mathfrak{E}}_{UU}]_{j\ell}=\mathcal{E}(U_j,U_\ell)\), \(j\neq \ell\), with \(\mathcal{E}(U_j,U_\ell)=\int_0^1 F_{U_j}^{-1}(t) F_{U_\ell}^{-1}(t) \, dt\), and \([\boldsymbol{\mathfrak{E}}_{UU}]_{jj}=\mathbb{E}(U_j^2)\), \(j,\ell=1,\dots,p\)

    • \(\boldsymbol{\Psi}=\text{Diag}(\mathbb{E}(U_1),\dots,\mathbb{E}(U_p))\)

References

Oliveira, M. R., Pinheiro, D., & Oliveira, L. (2025). Location and association measures for interval-valued data based on Mallows' distance. arXiv preprint arXiv:2407.05105. https://arxiv.org/abs/2407.05105

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 (normalized 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")

# Obtain parameters of the latent variables
credit_card_param <- get_latent_param(LatentCase = "General",
                                      LatentDist = "KDE",
                                      Umicro = credit_card_U)