methods_pspatreg {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 class 'pspatreg'
anova(object, ..., lrtest = TRUE)

## S3 method for class 'pspatreg'
coef(object, ...)

## S3 method for class 'pspatreg'
fitted(object, ...)

## S3 method for class 'pspatreg'
logLik(object, ..., REML = FALSE)

## S3 method for class 'pspatreg'
residuals(object, ...)

## S3 method for class 'pspatreg'
vcov(object, ..., bayesian = TRUE)

## S3 method for class 'pspatreg'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

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).

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

Author(s)

Roman Minguez	[e-mail]
Roberto Basile	[e-mail]
Maria Durban	[e-mail]
Gonzalo Espana-Heredia	[e-mail]

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)

#' ########### 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")