pspatreg (version 1.1.2)

methods_pspatreg: Methods for class pspatreg

Description

The anova function provides tables of fitted `pspatreg` models including information criteria (AIC and BIC), log-likelihood and degrees of freedom of each fitted model. The argument `lrtest` allows to perform LR tests between nested models. The print function is used to print short tables including the values of beta and spatial coefficients as well as p-values of significance test for each coefficient. This can be used as an alternative to summary.pspatreg when a brief output is needed. The rest of methods works in the usual way.

Usage

# S3 method for pspatreg
anova(object, ..., lrtest = TRUE)
# S3 method for pspatreg
coef(object, ...)
# S3 method for pspatreg
fitted(object, ...)
# S3 method for pspatreg
logLik(object, ..., REML = FALSE)
# S3 method for pspatreg
residuals(object, ...)
# S3 method for pspatreg
vcov(object, ..., bayesian = TRUE)
# S3 method for pspatreg
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Value

anova: An object of class anova. Can be printed with summary. If argument lrtest = TRUE (default), the object returned includes an LR test for nested models. In this case, a warning message is printed to emphasize that the LR test remains valid only for nested models.

coef: A numeric vector including spatial parameters and parameters corresponding to parametric covariates. Also includes fixed parameters for non-parametric covariates. Can be printed with print.

fitted: A numeric vector including fitted values for the dependent variable.

logLik: An object of class logLik. Can be printed with print. If argument REML = FALSE (default), the object returns the value of log-likelihood function in the optimum. If argument REML = TRUE, the object returns the value of restricted log-likelihood function in the optimum.

residuals: A numeric vector including residuals of the model.

vcov: A matrix including the covariance matrix for the estimated parameters. If argument bayesian = TRUE (default), the covariance matrix is computed using bayesian method. If argument bayesian = FALSE , the covariance matrix is computed using sandwich method. See Fahrmeir et al. (2021) for details.

print: No return value

Arguments

object

a `pspatreg` object created by pspatfit.

...

further arguments passed to or from other methods.

lrtest

logical value to compute likelihood ratio test for nested models in `anova` method. Default = `TRUE`

REML

logical value to get restricted log-likelihood instead of the usual log-likelihood. Default = `FALSE`

bayesian

logical value to get bayesian or frequentist covariance matrix for parametric terms. Default = `FALSE`

x

similar to object argument for print() and plot functions.

digits

number of digits to show in printed tables. Default: max(3L, getOption("digits") - 3L).

Author

Roman Minguez
Roberto Basile
Maria Durban
Gonzalo Espana-Heredia

References

• Fahrmeir, L.; Kneib, T.; Lang, S.; and Marx, B. (2021). Regression. Models, Methods and Applications (2nd Ed.). Springer.

Examples

library(pspatreg)
###############################################
# Examples using spatial data of Ames Houses.
###############################################
# Getting and preparing the data
library(spdep)
library(sf)
ames <- AmesHousing::make_ames() # Raw Ames Housing Data
ames_sf <- st_as_sf(ames, coords = c("Longitude", "Latitude"))
ames_sf$Longitude <- ames$Longitude
ames_sf$Latitude <- ames$Latitude
ames_sf$lnSale_Price <- log(ames_sf$Sale_Price)
ames_sf$lnLot_Area <- log(ames_sf$Lot_Area)
ames_sf$lnTotal_Bsmt_SF <- log(ames_sf$Total_Bsmt_SF+1)
ames_sf$lnGr_Liv_Area <- log(ames_sf$Gr_Liv_Area)
ames_sf1 <- ames_sf[(duplicated(ames_sf$Longitude) == FALSE), ]
####  GAM pure with pspatreg
form1 <- lnSale_Price ~ Fireplaces + Garage_Cars +
          pspl(lnLot_Area, nknots = 20) + 
          pspl(lnTotal_Bsmt_SF, nknots = 20) +
          pspl(lnGr_Liv_Area, nknots = 20)    
gampure <- pspatfit(form1, data = ames_sf1)
summary(gampure)
# \donttest{
#' ########### Constructing the spatial weights matrix
coord_sf1 <- cbind(ames_sf1$Longitude, ames_sf1$Latitude)
k5nb <- knn2nb(knearneigh(coord_sf1, k = 5, 
                          longlat = TRUE, use_kd_tree = FALSE), sym = TRUE)
lw_ames <- nb2listw(k5nb, style = "W", 
                  zero.policy = FALSE)

#####################  GAM + SAR Model
gamsar <- pspatfit(form1, data = ames_sf1, 
                   type = "sar", listw = lw_ames,
                   method = "Chebyshev")
summary(gamsar)

### Compare Models
anova(gampure, gamsar, lrtest = FALSE)
## logLikelihood 
logLik(gamsar)
## Restricted logLikelihood
logLik(gamsar, REML = TRUE)
## Parametric and spatial coefficients
print(gamsar)
coef(gamsar)
## Frequentist (sandwich) covariance matrix 
## (parametric terms)
vcov(gamsar, bayesian = FALSE)      
## Bayesian covariance matrix (parametric terms)
vcov(gamsar)
#####################################
#### Fitted Values and Residuals
plot(gamsar$fitted.values, 
     ames_sf1$lnSale_Price, 
     xlab = 'fitted values', 
     ylab = "unrate",
     type = "p", cex.lab = 1.3, 
     cex.main = 1.3,
     main = "Fitted Values gamsar model")      
plot(gamsar$fitted.values, gamsar$residuals, 
     xlab = 'fitted values', ylab = "residuals",
     type = "p", cex.lab = 1.3, cex.main=1.3,
     main = "Residuals geospsar model")
# }