impactspar {pspatreg}

Compute direct, indirect and total impacts for continous parametric covariates.

Description

Compute direct, indirect and total impacts for parametric covariates included in a semiparametric spatial or spatio-temporal model. The models can be of type ps-sar, ps-sarar, ps-sdm, ps-sdem or ps-slx.

Usage

impactspar(obj, ..., tr = NULL, R = 1000, listw = NULL, tol = 1e-06, Q = NULL)

Arguments

obj

A 'pspatreg' object created by pspatfit.

...

Arguments passed through to methods in the coda package

tr

A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised

R

If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects; the objects are used for convenience but are not output by an MCMC process

listw

If tr is not given, a spatial weights object as created by nb2listw; they must be the same spatial weights as were used in fitting the spatial regression, but do not have to be row-standardised

tol

Argument passed to mvrnorm: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix

Q

default NULL, else an integer number of cumulative power series impacts to calculate if tr is given

Details

This function is similar to the impacts method used in spatialreg. package. The function impactspar obtains the three type of impacts (total, direct and indirect) together with a measure of statistical significance, according to the randomization approach described in LeSage and Pace (2009). Briefly, they suggest to obtain a sequence of nsim random matrices using a multivariate normal distribution N(0; Sigma), being Sigma the estimated covariance matrix of the fitted beta for parametric covariates and spatial parameters of the model. These random matrices, combined with the values of the fitted beta for parametric covariates and the estimated values of the spatial parameters, are used to obtain simulated values. The function impactspar obtains the standard deviations using the nsim simulated impacts in the randomization procedure, which are used to test the significance of the estimated impacts for the original data. Finally, if the spatial model is type = "slx" or "sdem", then there is no need to simulate to make inference of the impacts. The standard errors of the impacts are computed directly using the Sigma matrix of the estimated covariances of beta and spatial parameters.

Value

An object of class impactspar.pspatreg. Can be printed with summary.

If type = "sar", "sdm", "sarar", the object returned is a list with 4 objects including the type of model and three matrices including the simulated total, direct and indirect impacts:

type	Type of spatial econometric model.
mimpactstot	Matrix including simulated total impacts for each variable in rows.
mimpactsdir	Matrix including simulated direct impacts for each variable in rows.
mimpactsind	Matrix including simulated indirect impacts for each variable in rows.

If type = "slx", "sdem" the object returned is a list with 5 objects including the type of model and four matrices including the computed total, direct and indirect impacts, the standard errors, the z-values and p-values of each type of impact:

type	Type of spatial econometric model.
mimpact	Matrix including computed total, direct and indirect impacts for each variable in rows.
semimpact	Matrix including standard errors of total, direct and indirect impacts for each variable in rows.
zvalmimpact	Matrix including z-values of total, direct and indirect impacts for each variable in rows.
pvalmimpact	Matrix including p-values of total, direct and indirect impacts for each variable in rows.

References

• LeSage, J. and Pace, K. (2009). Introduction to Spatial Econometrics. CRC Press, Boca Raton.

See Also

• pspatfit estimate spatial or spatio-temporal semiparametric ps-sar, ps-sem, ps-sarar, ps-slx or ps-durbin regression models.

• impactsnopar compute total, direct and indirect impact functions for non-parametric continuous covariates.

• fit_terms compute smooth term functions for non-parametric continuous covariates.

• impacts similar function in spdep package to compute impacts in spatial parametric econometric models.

Examples

################################################
#### Examples using a panel data of rate of
##### unemployment for 103 Italian provinces in period 1996-2014.
library(pspatreg)
data(unemp_it, package = "pspatreg")
## Wsp_it is a matrix. Create a neighboord list 
lwsp_it <- spdep::mat2listw(Wsp_it)
## short sample for spatial pure case (2d)
########  No Spatial Trend: PSAR including a spatial 
########  lag of the dependent variable
form1 <- unrate ~ partrate + agri + cons + empgrowth +
                 pspl(serv, nknots = 15) 
### example with type = "sar"                   
gamsar <- pspatfit(form1, 
                   data = unemp_it, 
                   type = "sar", 
                   listw = lwsp_it)
summary(gamsar)
###### Parametric Total, Direct and Indirect Effects
imp_parvar <- impactspar(gamsar, listw = lwsp_it)
summary(imp_parvar)

### example with type = "slx"                   

gamslx <- pspatfit(form1, 
                   data = unemp_it, 
                   type = "slx", 
                   listw = lwsp_it)
                   
summary(gamslx)
###### Parametric Total, Direct and Indirect Effects
imp_parvarslx <- impactspar(gamslx, listw = lwsp_it)
summary(imp_parvarslx)