sphstat.modelling module

Functions for correlation, regression, temporal association

• xcorrrandomsamples() calculates the cross-correlation between two samples

• samplecorrelation() calculates the sample cross-correlation

• jackknife_corrci() calculates a jeckknife estimate of the CI for the correlation coefficient

• xcorrsamplevariable() calculates the correlation of a sample with a variable

• regresscircular() calculates a regression model for a circular variable

• isnotseriallyassociated() tests the null hypothesis that the samples are independent as opposed to being temporally associated

sphstat.modelling.isnotseriallyassociated(samplecart: dict, alpha: float = 0.05)

Test the null hypothesis that the observations are independent as opposed to having serial association 1

Parameters

• samplecart (dict) – Sample to be used in the computations in ‘cart’ form

• alpha (float) – Type-I error level to be used in the test

Returns

Dictionary containing the keys: - Sstar: The test statistic (float) - cval: Critical value (float) - testresult: Test result (bool), False if the observations are serially associated

Return type

dict

1

Watson, G. S. & Beran, R. J. (1967). Testing a sequence of unit vectors for randomness. J. Geophys. Res. 72, 5655-5659.

sphstat.modelling.jackknife_corrci(samplecart1: dict, samplecart2: dict, alpha: float = 0.05) → tuple

Jackknife method for calculating an approximate confidence interval for correlation coefficient

Parameters

• samplecart1 (dict) – Sample 1 to be used in the computations in ‘cart’ form

• samplecart2 (dict) – Sample 2 to be used in the computations in ‘cart’ form

• alpha (float) – (1-alpha)% CI is calculated

Returns

• psijhat: Unbiased estimate using the jackknife method (float)

• ci: (1-alpha)% confidence interval (tuple)

Return type

tuple

sphstat.modelling.regresscircular(samplecart: dict, thetas: list, alpha0: float, thr: float = 0.01) → tuple

Regression of a random unit vector on a circular variable 2

Parameters

• samplecart (dict) – Sample to be used in the computations in ‘cart’ form

• thetas (list) – List containing a circular variable

• alpha0 (float) – Initial angle for the iterations

• thr (float) – Stopping condition for the iterations (Defaults to 1e-15)

Returns

• Uhat: Regression matrix (np.array)

• w: np.array([0, 0, 1])

• alphahat: The angle to be used in the regression model

• fitmodel: Function to predict a value for a given variable [Callable]

Return type

tuple

2

Jupp, P. E. & Mardia, K. V. (1980). A general correlation coefficient for directional data and related regression problems. Biometrika 67, 163-173.

sphstat.modelling.samplecorrelation(samplecart1: dict, samplecart2: dict, indlist: Optional[list] = None) → float

Correlation of two samples

Parameters

• samplecart1 (dict) – Sample 1 to be used in the computations in ‘cart’ form

• samplecart2 (dict) – Sample 2 to be used in the computations in ‘cart’ form

• indlist – Indices to use for the second sample (use only for the permutation test)

Returns

Sample cross correlation

Return type

float

sphstat.modelling.xcorrrandomsamples(samplecart1: dict, samplecart2: dict, numperms: int, htype: str = '=', alpha: float = 0.05) → dict

Correlation coefficient of two random unit vectors and hypothesis test given two samples 3

Parameters

• samplecart1 (dict) – Sample 1 to be used in the computations in ‘cart’ form

• samplecart2 (dict) – Sample 2 to be used in the computations in ‘cart’ form

• numperms (int) – Number of permutations to be used in the permutation test

• htype – Null hypothesis type, ‘!=’ for H0: rho!=0 (no correlation), ‘>’ for H0: rho > 0 (positive correlation), ‘<’ for H0: rho < 0 (negative correlation)

• htype – str

• alpha (float) – (1-alpha)% CI is calculated

Returns

Dictionary containing: - rhohat: Correlation coefficient estimate (float) - std: Standard deviation from jackknife estimate (float) - cval’: Critical values (tuple) - ci: (1-alpha)% CI for the correlation coefficient (tuple) - testresult: Hypothesis test result (bool)

Return type

dict

3

Fisher, N. I. & Lee, A. J. (1986). Correlation coefficients for random variables on a unit sphere or hypersphere.

sphstat.modelling.xcorrsamplevariable(samplecart: dict, variable: list, alpha: float = 0.05)

Correlation between a random unit vector or axis and another random variable Tests the null hypothesis (H0) that the spherical sample and the variable are uncorrelated 4

Parameters

• samplecart (dict) – Sample to be used in the computations in ‘cart’ form

• variable (list) – List of floats or 1-D numpy arrays representing a variable associated with the points in the sample

• alpha (float) – Type-I error level to be used in the test

Returns

Dictionary containing… - rhohatg: Correlation coefficient (float) - teststat: Test statistics (float) - cval: Critical value used in the test (float) - testresult: Result of the hypothesis test (bool)

4

Jupp, P. E. & Mardia, K. V. (1980). A general correlation coefficient for directional data and related regression problems. Biometrika 67, 163-173.