adespatial (version 0.3-24)

Cperiodogram: Contingency periodogram

Description

Function to compute a contingency periodogram for a univariate series of qualitative data

Usage

Cperiodogram(x, T1 = 2, T2 = NULL, nperm = NULL, alpha = 0.05, graph = TRUE)

Value

A table with the statistics for the selected periods:

• Wilks' chi-square statistic (Wilks.chisq)

• information in common (B),

• degrees of freedom (df),

• p-value (prob)

Confidence interval limits:

• critical value of B without correction (B.crit),

• critical value of B with Bonferroni correction based on the number of periods studied in the periodogram (B.crit.Bonf),

• critical value of B with progressive Bonferroni correction (B.prog.Bonf).

Arguments

x

a qualitative variable (factor)

T1

first period included in the calculations (default: T1 = 2)

T2

last period included in the calculations (default: T2 = n/2)

nperm

Number of permutations for the chi-square test. For chi-square tests using the chi- square distribution, use the default nperm=NULL

alpha

significance level for computation of the confidence limits

graph

a logical indicating if a graph is requested, by default TRUE.

Author

Pierre Legendre

Details

The contingency periodogram of Legendre et al. (1981) identifies periodic components in qualitative data vectors. The vector may contain classes of a qualitative variable or the classes obtained by hierarchical clustering or partitioning of a multivariate data table. The method is also described in Legendre & Legendre (2012). The optional graph produced by the function shows the following information:

• In red: the B statistics (information in common).

• In blue: Confidence limits for B without correction.

• In green: Bonferroni-corrected limits of the confidence intervals.

• In black: Confidence limits with progressive Bonferroni correction.

References

Legendre, L., M. Fréchette & P. Legendre. 1981. The contingency periodogram: a method of identifying rhythms in series on nonmetric ecological data. Journal of Ecology 69: 965-979.

Legendre, P. and Legendre, L. 2012. Numerical Ecology. 3rd English ed. Elsevier, Amsterdam

Examples

# Data from the numerical example of Subsection 12.4.2 of Legendre and Legendre (2012).
test.vec <- c(1,1,2,3,3,2,1,2,3,2,1,1,2,3,3,1)
# Periodogram with tests using the chi-square distribution
res <- Cperiodogram(test.vec)
# Periodogram with permutation tests
res <- Cperiodogram(test.vec, nperm=2000, graph=FALSE)