fit_terms: Compute terms for non-parametric spatial (2d) or...

In rominsal/sptpsar: Spatio-Temporal Semiparametric Models with Spatial Lags

Compute terms for non-parametric spatial (2d) or spatio-temporal (3d) trends and for smooth functions of continous non-parametric covariates in PS-SAR regression models.

Description

The fit_terms function compute both:

• Non-parametric spatial (2d) or spatio-temporal (3d) trends including the decomposition in main and interaction trends when the model is ANOVA.

• Smooth functions f(x_i) for non-parametric covariates in semiparametric models. It also includes standard errors and the decomposition of each non-parametric term in fixed and random parts.

Usage

fit_terms(sptsarfit, variables)

Arguments

sptsarfit	psar object fitted using psar function.
variables	vector including names of non-parametric covariates. To fit the terms of non-parametric spatial (2d) or spatio-temporal (3d) trend this argument must be set equal to spttrend.

Value

A list including:

fitted_terms	Matrix including terms in columns.
se_fitted_terms	Matrix including standard errors of terms in columns.
fitted_terms_fixed	Matrix including fixed part of terms in columns.
se_fitted_terms_fixed	Matrix including standard errors of fixed part of terms in columns.
fitted_terms_random	Matrix including random part of terms in columns.
se_fitted_terms_random	Matrix including standard errors of random part of terms in columns.

This object can be used as an argument of plot_terms function to make plots of both non-parametric trends and smooth functions of covariates. See examples below.

Author(s)

Roman Minguez [e-mail] #'

References

• Lee, D. and Durbán, M. (2011). P-Spline ANOVA Type Interaction Models for Spatio-Temporal Smoothing. Statistical Modelling, (11), 49-69.

• Wood, S.N. (2017). Generalized Additive Models. An Introduction with R (second edition). CRC Press, Boca Raton.

See Also

• psar estimate spatial or spatio-temporal semiparametric PS-SAR regression models.

• plot_terms plot smooth functions of non-parametric covariates.

• plot_main_spt plot main non-parametric functions in ANOVA trends.

Examples

################################################
 ###################### Examples using a panel data of rate of
 ###################### unemployment for 103 Italian provinces in period 1996-2014.
library(sptpsar)
data(unemp_it); Wsp <- Wsp_it
######################  No Spatial Trend: PSAR including a spatial 
######################  lag of the dependent variable
form1 <- unrate ~ partrate + agri + cons +
                 pspl(serv,nknots=15) +
                 pspl(empgrowth,nknots=20) 
 gamsar <- psar(form1,data=unemp_it,sar=TRUE,Wsp=Wsp_it)
 summary(gamsar)
 ######################  Fit non-parametric terms (spatial trend must be name "spttrend")
 list_varnopar <- c("serv","empgrowth")
 terms_nopar <- fit_terms(gamsar,list_varnopar)
 ######################  Plot non-parametric terms
 plot_terms(terms_nopar,unemp_it)
 
 ###############################################
 Examples of terms corresponding to spatial (2d) or 
            spatio-temporal (3d) trends
 ###############################################
 
 # Spatial (2d) semiparametric ANOVA model without spatial lag
 # Interaction term f12 with nested basis
form3 <- unrate ~ partrate + agri + cons +
                  pspl(serv,nknots=15) + pspl(empgrowth,nknots=20) +
                  pspt(long,lat,nknots=c(20,20),psanova=TRUE,
                  nest_sp1=c(1,2),nest_sp2=c(1,2))
# Spatial trend fixed for period 1996-2014
geospanova <- psar(form3,data=unemp_it)
summary(geospanova)
### Plot spatial trend (ANOVA)
spttrend <- fit_terms(geospanova,"spttrend")
lon <- scale(unemp_it$long); lat <- scale(unemp_it$lat)
### Plot main effects
plot_main_spt(spttrend,sp1=lon,sp2=lat,nT=19)

#'  ###############################################
 # Spatio-temporal (3d) semiparametric ANOVA model without spatial lag
 # Interaction terms f12,f1t,f2t and f12t with nested basis
 # Remark: It is necessary to include ntime as argument
 # Remark: nest_sp1, nest_sp2 and nest_time must be divisors of nknots
 form4 <- unrate ~ partrate + agri + cons +
                   pspl(serv,nknots=15) + pspl(empgrowth,nknots=20) +
                   pspt(long,lat,year,nknots=c(18,18,8),psanova=TRUE,
                   nest_sp1=c(1,2,3),nest_sp2=c(1,2,3),
                   nest_time=c(1,2,2),ntime=19)
 sptanova <- psar(form4,data=unemp_it,
                  control=list(thr=1e-2,maxit=200,trace=FALSE))
 summary(sptanova)
 ### Plot spatial trend (ANOVA)
 spttrend <- fit_terms(sptanova,"spttrend")
 lon <- scale(unemp_it$long); lat <- scale(unemp_it$lat)
 time <- unemp_it$year
 ### Plot main effects
 plot_main_spt(spttrend,sp1=lon,sp2=lat,time=time,nT=19)
 
 @export
 

rominsal/sptpsar documentation built on June 1, 2022, 2:03 a.m.