Rey's (2001) spatial Markov chain: one transition matrix for each class of a country's spatial lag – the average class of its neighbours – so you can ask whether a poor country among poor neighbours is less likely to move up than one among rich neighbours. A homogeneity test says whether the conditional matrices differ from the pooled one.
Usage
spatial_markov(
data,
value,
weights = NULL,
n_classes = 5,
classes = c("quantile", "relative"),
step = 1
)Arguments
- data
A panel with
iso3c,yearand the value column.- value
The column to classify (unquoted), such as GDP per capita.
- weights
A
country_weights()object;NULL(default) is k-nearest neighbours (k = 5), so islands take part.- n_classes
Number of classes (default
5).- classes
"quantile"(default) cuts each year at its own quantiles, so a class is a rank band;"relative"divides each value by its year's cross-country mean and cuts at the pooled quantiles of those ratios, so a class is a band of relative income that can fill or empty over time.- step
Years between the two observations of a transition (default
1); keyed on the year, so a gap in a country's series gives no transition rather than a longer one.
Value
A tibble of lag_class, from, to, n and p, with the
attribute test: a tibble of the likelihood-ratio and chi-square
homogeneity statistics, their degrees of freedom and p-values
(Bickenbach & Bode 2003), where cells with no transitions do not count
toward the degrees of freedom (Kang & Rey 2018).
References
Rey, S. J. (2001). Spatial empirics for economic growth and convergence. Geographical Analysis 33(3), 195-214. doi:10.1111/j.1538-4632.2001.tb00444.x
Bickenbach, F. & Bode, E. (2003). Evaluating the Markov property in studies of economic convergence. International Regional Science Review 26(3), 363-392. doi:10.1177/0160017603253789
Kang, W. & Rey, S. J. (2018). Conditional and joint tests for spatial effects in discrete Markov chain models of regional income distribution dynamics. The Annals of Regional Science 61(1), 73-93. doi:10.1007/s00168-017-0859-9
Examples
# \donttest{
set.seed(1)
iso <- countryatlas::world_snapshot$countries$iso3c
pan <- expand.grid(iso3c = iso, year = 2010:2015, stringsAsFactors = FALSE)
pan$v <- exp(stats::rnorm(nrow(pan)))
spatial_markov(pan, v, n_classes = 3)
#> # A tibble: 27 × 5
#> lag_class from to n p
#> <int> <int> <int> <int> <dbl>
#> 1 1 1 1 48 0.397
#> 2 1 2 1 35 0.28
#> 3 1 3 1 40 0.351
#> 4 1 1 2 40 0.331
#> 5 1 2 2 46 0.368
#> 6 1 3 2 41 0.360
#> 7 1 1 3 33 0.273
#> 8 1 2 3 44 0.352
#> 9 1 3 3 33 0.289
#> 10 2 1 1 33 0.282
#> # ℹ 17 more rows
# }