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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:

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

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

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

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.

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 LatentDist="KDE" or estimate.DistParam=TRUE.

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 with the parameters 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:

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

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

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
credit_agrby<-paste(CreditCard_microdata$Name,CreditCard_microdata$Month,sep = "_")
credit_card_U<-get_latent_var(CreditCard_microdata[,3:7], CreditCard_min_max, credit_agrby, 
                              agrlevels = row.names(CreditCard_min_max), Seq="LbUb_VarbyVar")
credit_card_param<-get_latent_param(LatentCase="General",LatentDist="KDE",Umicro=credit_card_U)