miexp is the null expectation E(I) = -1/(n - 1); mivar the null
variance from the weights constants S0, S1, S2 under normality, or
under randomisation when the sample kurtosis b2 is given; mizval the
standardised z = (I - E(I)) / sqrt(Var(I)) with its normal p-value;
minorm combines the three. miorig and mirand compute Moran's I
of y with the normality and randomisation moments
(spdep::moran.test), mimc the permutation test (spdep::moran.mc,
Philox-driven shuffles identical to the Python arm), miols the exact
OLS-residual test (spdep::lm.morantest), miml Moran's I of residuals
of a maximum-likelihood spatial model with randomisation moments, and
miiv the Anselin-Kelejian (1997) test for 2SLS residuals.
Usage
miexp(n)
mivar(n, S0, S1, S2, b2 = NULL)
mizval(I, E_I, Var_I, alternative = "greater")
minorm(I, n, S0, S1, S2, b2 = NULL, alternative = "greater")
miorig(y, W, alternative = "greater")
mirand(y, W, alternative = "greater")
mimc(y, W, nsim = 99, seed = 0)
miols(resid, W, X = NULL)
miml(resid, W, alternative = "greater")
miiv(resid, W, Z, H)Arguments
- n
Number of observations.
- S0
Sum of the weights.
- S1
Half the sum of squared symmetrised weights.
- S2
Sum of squared row plus column sums.
- b2
Sample kurtosis; NULL selects the normality variance.
- I
Moran's I.
- E_I
Expectation of I.
- Var_I
Variance of I.
- alternative
One of "greater", "less" or "two.sided".
- y
Numeric vector of observations.
- W
Spatial weights matrix.
- nsim
Number of permutations.
- seed
Philox seed.
- resid
Residual vector.
- X
Design matrix of the OLS fit (default intercept only).
- Z
Regressor matrix of the 2SLS fit.
- H
Instrument matrix of the 2SLS fit.
Value
A list with statistic, p_value, expected, variance and
method-specific components (for miiv, statistic is the AK
chi-square and moran_i the residual Moran's I).
References
Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika 37, 17-23. Cliff, A. D. and Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion. Anselin, L. and Kelejian, H. H. (1997). Testing for spatial error autocorrelation in the presence of endogenous regressors. International Regional Science Review 20, 153-182.