Front ends for the spatial lag model \(y = \rho W y + X\beta + e\); R
arm of the Python modules morie.fn.sar*. Sardet and
Sarjac: the log-Jacobian \(\log|I - \rho W|\) by LU.
Sarlrt: likelihood ratio \(2(l_1 - l_0)\) against chi-square.
Sarwald: \((\rho/se)^2\) against chi-square(1). Sarr2:
Nagelkerke's rescaled R-squared. Sarfilt: the filter
\((I - \rho W)y\). Sarres: Moran's I of residuals, exact test
(as spdep::lm.morantest) when the design is given. Sarsc:
LM (score) test of \(\rho = 0\) after OLS with its error-robust form.
Sarimp, Sarspil: LeSage-Pace average direct, indirect and
total impacts and the indirect/direct ratio. Sarsim: impacts of
parameter draws from \(N((\rho, \beta), V)\) (Philox normals).
Sarvar: inverse analytic information matrix of
\((\beta, \rho, \sigma^2)\). Sarboot: residual-bootstrap
percentile interval for \(\rho\) (Philox resampling).
Usage
Sardet(W, rho)
Sarjac(W, rho)
Sarlrt(ll_sar, ll_ols, df = 1)
Sarwald(rho, se_rho)
Sarr2(ll_model, ll_null, n)
Sarfilt(y, W, rho = 0.3)
Sarres(resid, W, X = NULL)
Sarsc(y, X, W)
Sarimp(coef, rho, W)
Sarspil(coef, rho, W)
Sarsim(coef, rho, W, nsim = 99, vcov = NULL, seed = 0)
Sarvar(X, W, rho, sigma2, beta)
Sarboot(y, X, W, B = 99, seed = 0, level = 0.95)Arguments
- W
Spatial weights matrix.
- rho
Spatial lag parameter.
- ll_sar, ll_ols
Log-likelihoods of the SAR and the OLS model.
- df
Degrees of freedom.
- se_rho
Standard error of
rho.- ll_model, ll_null
Log-likelihoods of the model and the null model.
- n
Number of observations.
- y
Response (or series to filter).
- resid
Model residuals.
- X
Design matrix including any intercept column (optional for
Sarres).- coef
Slopes of the lag model, without intercept.
- nsim
Number of simulation draws.
- vcov
Covariance of
c(rho, coef).- seed
Philox seed.
- sigma2
Error variance.
- beta
Regression coefficients including the intercept.
- B
Bootstrap replicates.
- level
Confidence level.
Value
A list whose statistic is the headline value, with the
components of the Python result's extra.
References
Ord, K. (1975). Estimation methods for models of spatial interaction. Journal of the American Statistical Association 70, 120-126.
Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer, Dordrecht.
Anselin, L., Bera, A. K., Florax, R. and Yoon, M. J. (1996). Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics 26, 77-104.
LeSage, J. and Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press, Boca Raton.
Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination. Biometrika 78, 691-692.
Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall.