regimes {hspm}

Estimation of regimes models

Description

The function regimes deals with the estimation of regime models. Most of the times the variable identifying the regimes reveals some spatial aspects of the data (e.g., administrative boundaries).

Usage

regimes(formula, data, rgv = NULL, vc = c("homoskedastic", "groupwise"))

Arguments

formula

a symbolic description of the model of the form y ~ x_f | x_v where y is the dependent variable, x_f are the regressors that do not vary by regimes and x_v are the regressors that vary by regimes

data

the data of class data.frame.

rgv

an object of class formula to identify the regime variables

vc

one of c("homoskedastic", "groupwise"). If groupwise, the model VC matrix is estimated by weighted least square.

Details

For convenience and without loss of generality, we assume the presence of only two regimes. In this case, the basic (non-spatial) is:

y = \begin{bmatrix} X_1& 0 \\ 0 & X_2 \\ \end{bmatrix} \begin{bmatrix} \beta_1 \\ \beta_2 \\ \end{bmatrix} + X\beta + \varepsilon

where y = [y_1^\prime,y_2^\prime]^\prime, and the n_1 \times 1 vector y_1 contains the observations on the dependent variable for the first regime, and the n_2 \times 1 vector y_2 (with n_1 + n_2 = n) contains the observations on the dependent variable for the second regime. The n_1 \times k matrix X_1 and the n_2 \times k matrix X_2 are blocks of a block diagonal matrix, the vectors of parameters \beta_1 and \beta_2 have dimension k_1 \times 1 and k_2 \times 1, respectively, X is the n \times p matrix of regressors that do not vary by regime, \beta is a p\times 1 vector of parameters and \varepsilon = [\varepsilon_1^\prime,\varepsilon_2^\prime]^\prime is the n\times 1 vector of innovations.

• If vc = "homoskedastic", the model is estimated by OLS.

• If vc = "groupwise", the model is estimated in two steps. In the first step, the model is estimated by OLS. In the second step, the inverse of the (groupwise) residuals from the first step are employed as weights in a weighted least square procedure.

Value

An object of class lm and spregimes.

Author(s)

Gianfranco Piras and Mauricio Sarrias

Examples

data("baltim")
form   <- PRICE  ~ NROOM + NBATH + PATIO + FIREPL + AC + GAR + AGE + LOTSZ + SQFT
split  <- ~ CITCOU
mod <- regimes(formula = form, data = baltim, rgv = split, vc = "groupwise")
summary(mod)
form <- PRICE  ~ AC + AGE + NROOM + PATIO + FIREPL + SQFT | NBATH + GAR + LOTSZ - 1
mod <- regimes(form, baltim, split, vc = "homoskedastic")
summary(mod)