fit_terms {pspatreg}

Compute terms of the non-parametric covariates in the semiparametric 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(object, variables, intercept = FALSE)

Arguments

object

object fitted using pspatfit 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'. See examples in this function.

intercept

add intercept to fitted term. Default = FALSE.

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

References

• Lee, D. and Durban, M. (2011). P-Spline ANOVA Type Interaction Models for Spatio-Temporal Smoothing. Statistical Modelling, (11), 49-69. <doi:10.1177/1471082X1001100104>

• Eilers, P. and Marx, B. (2021). Practical Smoothing. The Joys of P-Splines. Cambridge University Press.

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

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

See Also

• pspatfit estimate spatial or spatio-temporal semiparametric regression models. The model can be of type ps-sim, ps-sar, ps-slx, ps-sem, ps-sdm or ps-sarar.

• plot_terms plot smooth functions of non-parametric covariates.

Examples

###################### Examples using a panel data of rate of unemployment 
###################### in 103 Italian provinces during the period 1996-2014.
library(pspatreg)
data(unemp_it, package = "pspatreg")
lwsp_it <- spdep::mat2listw(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 <- pspatfit(form1, data = unemp_it, 
                    type = "sar", listw = lwsp_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)