Package 'arkhaia'

Description

For a matrix of cross-tabulated counts of observations, computes the Cressie-Read power-divergence statistic according to the selection of a parameter $\lambda$ (Cressie and Read 1984; Read and Cressie 1988).

Usage

CR(x, lambda = 2/3)

## S3 method for class 'matrix'
CR(x, lambda = 2/3)

## S3 method for class 'data.frame'
CR(x, lambda = 2/3)

## S3 method for class 'xtabs'
CR(x, lambda = 2/3)

## S3 method for class 'table'
CR(x, lambda = 2/3)

Arguments

Value

The Cressie-Read power-divergence statistic.

References

Cressie NAC, Read TRC (1984). “Multinomial Goodness-of-Fit Tests.” Journal of the Royal Statistical Society. Series B (Methodological), 46, 440–464. doi:10.1111/j.2517-6161.1984.tb01318.x.

Read TRC, Cressie NAC (1988). Goodness-of-Fit Statistics for Discrete Multivariate Data. Springer, New York.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)
x3 <- c(0, 0, 2, 81, 11)

x <- matrix(c(x1, x2, x3), ncol = 3)

CR(x)
CR(x, lambda = 1)

Description

For multiple time-indexed observations and a number of events, $r = 1, ldots, n_r$, that occur at a given time index, this function performs a regression of the form $x(t) = \beta_0 + \sum_{r = 1}^{n_r} \gamma t I(t \leq t_r ) e^{-\lambda t}$, where $I(t \geq t_r )$ is an indicator function equaling 1 if $t \geq t_r$. Estimation of $\gamma$, $\lambda$, and $\beta_0$ is performed numerically on specified ranges of potential values. The intercept term is not used where cases where a zero intercept is expected (e.g., standardized observations).

Usage

dtem(
  x,
  events,
  gamma = c(-10, 10),
  lambda = c(0, 5),
  intercept = FALSE,
  incr = 0.01
)

## S3 method for class 'time_series'
dtem(
  x,
  events,
  gamma = c(-10, 10),
  lambda = c(0, 5),
  intercept = FALSE,
  incr = 0.01
)

Arguments

Value

A list containing

• A vector of coefficients and the residual sum of squares.

• A matrix of the residual sum of squares for samples within the ranges of gamma and lambda.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

# generate example of positive trend (gamma = 2) 
# after event with slow decay (lambda = 0.05)
t_ <- runif(100, 0, 100)
events <- c(0, 54, 89)
gam <- 2
lam <- 0.05
x_ev1 <-  (t_ - events[1]) * gam  * exp(- lam * (t_ - events[1]))
x_ev2 <-  (t_ - events[2]) * gam  * exp(- lam * (t_ - events[2]))
x_ev3 <-  (t_ - events[3]) * gam  * exp(- lam * (t_ - events[3]))
x_ev1[t_ < events[1]] <- 0
x_ev2[t_ < events[2]] <- 0
x_ev3[t_ < events[3]] <- 0
y <- x_ev1 + x_ev2 + x_ev3 + rnorm(length(t_), 0, 0.25)
dat <- time_series(t = t_, x = y)

# fit model
res <- dtem(dat, events, gamma = c(-2.5,2.5), lam = c(0,0.1))

# coefficients
res$coefs

Description

Given a contingency table of cross-tabulated counts, with contexts along the columns and types along rows, this function estimates the distribution of effect sizes between pairs of "related" assemblages (determined a priori), as compared against a distribtion of "unrelated" assemblages (if not specified, are supplied as all pairs which are not included in the "related" set). Hence, the practical significance of the level of homogeneity between related deposits is evaluated against that of unrelated deposits.

Usage

homogeneity(x, related = NULL, unrelated = NULL, direction = "UW")

## S3 method for class 'effect_sizes'
homogeneity(x, related = NULL, unrelated = NULL, direction = "UW")

Arguments

Value

A list of results:

11

• n - A vector of the number of related and unrelated pairs of contexts, respectively $n_W$ and $n_U$.

• U - The effect sizes between unrelated pairs of contexts.

• W - The effect sizes between related pairs of contexts.

• Q - The quantile indicating the proportion of related contexts more homogenous than unrelated contexts (if direction is "UW"); less homogenous if direction is set to "UW".

• D - The distribution of differences, $D_{ij} = U_j - W_i$, if direction is set to "UW". The proportion of $D > 0$ is equivalent to the mean of Q.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)
x3 <- c(0, 0, 2, 81, 11)
x4 <- c(3, 18, 9, 0, 23)
x <- matrix(c(x1, x2, x3, x4), ncol = 4)
colnames(x) <- c("surface1", "subsurface1", "surface2", "subsurface2")
rownames(x) <- LETTERS[1:5]

# related pairs
W_contexts <- matrix(c("surface1", "surface2", "subsurface1", "subsurface2"), ncol = 2)

# unrelated pairs (will be automatically created if left NULL)
U_contexts <- matrix(c("surface1", "surface1", "surface2", "subsurface1",
                       "surface2","subsurface2", "surface1", "subsurface2"), ncol = 2)

effect_sizes <- VB_pair(x)
homogeneity(effect_sizes, related = W_contexts, unrelated = U_contexts) 
homogeneity(effect_sizes, related = W_contexts)

Description

To evaluate the stability of estimates of effect sizes between archaeological contexts in light of the inclusion or exclusion of types and contexts, this routine computes the homogeneity of related assemblages iteratively in two ways, first by leaving out a type on each iteration and second by leaving out a context on each iteration. For details on the arguments, see also homogeneity and VB).

Usage

homogeneity_LOO(
  x,
  related = NULL,
  unrelated = NULL,
  direction = "UW",
  lambda = 2/3
)

## S3 method for class 'matrix'
homogeneity_LOO(
  x,
  related = NULL,
  unrelated = NULL,
  direction = "UW",
  lambda = 2/3
)

## S3 method for class 'data.frame'
homogeneity_LOO(
  x,
  related = NULL,
  unrelated = NULL,
  direction = "UW",
  lambda = 2/3
)

## S3 method for class 'table'
homogeneity_LOO(
  x,
  related = NULL,
  unrelated = NULL,
  direction = "UW",
  lambda = 2/3
)

## S3 method for class 'xtabs'
homogeneity_LOO(
  x,
  related = NULL,
  unrelated = NULL,
  direction = "UW",
  lambda = 2/3
)

Arguments

Value

A list containing:

• EQ - The mean quantile expressing the degree of homogeneity among related contexts.

• EQ_T_mean - The mean quantile upon iterating over the omission of each type (of the LOO samples).

• EQ_T_var - The variance of the LOO type samples.

• EQ_C_mean - The mean quantile upon iterating over the omission of each context.

• EQ_C_var - The variance of the LOO context samples.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)
x3 <- c(0, 0, 2, 81, 11)
x4 <- c(3, 18, 9, 0, 23)
x <- matrix(c(x1, x2, x3, x4), ncol = 4)
colnames(x) <- c("surface1", "subsurface1", "surface2", "subsurface2")
rownames(x) <- LETTERS[1:5]

# related pairs
W_contexts <- matrix(c("surface1", "surface2", "subsurface1", "subsurface2"), ncol = 2)

# unrelated pairs (will be automatically created if left NULL)
U_contexts <- matrix(c("surface1", "surface1", "surface2", "subsurface1",
                       "surface2","subsurface2", "surface1", "subsurface2"), ncol = 2)

homogeneity_LOO(x, related = W_contexts, unrelated = U_contexts)

Description

For two one-dimensional temporal point processes $X_1$ and $X_2$, this function estimates the condition of the two processes becoming "integrated in distribution over time" (i.d.t.) at a moment in time $t$. This is achieved by computing the Kolmogorov-Smirnov distance $D$ between their empirical culumative distribution functions (e.c.d.f.), as a function $d(t,h)$ that encompasses observations on the support $(t-h,t+h)$. For practical significance in the estimation of $d$, Monte Carlo permutation of samples is used to estimate the probability that the observed value of $d$ is greater than the distribution of permuted samples (i.e., that observations are interchangable between $X_1$ and $X_2$).

Usage

idt_ks(x1, x2 = NULL, stat = FALSE, incr = 0.5, perm = FALSE, n_perm = 1e+05)

## S3 method for class 'numeric'
idt_ks(x1, x2 = NULL, stat = FALSE, incr = 0.5, perm = FALSE, n_perm = 1e+05)

## S3 method for class 'list'
idt_ks(x1, x2 = NULL, stat = FALSE, incr = 0.5, perm = FALSE, n_perm = 1e+06)

Arguments

Details

The Rcpp-based function ks_arkhaia relied upon for faster estimation of the KS distance than ks.test.

Value

A list containing a data frame two vectors x1 and x2, the probability that Monte Carlo permutation of samples results in a lower distance than the one obtained. For a list of vectors input in x1, a matrix of probabilities pairwise between all vectors.

Description

For two one-dimensional point processes, this function computes their Wasserstein R1 distances as a function $d(t,h)$, which encompasses observations on the support $(t-h,t+h)$. Monte Carlo permutation of samples is used to estimate the probability that the obtain distances is of practical signficance.

Usage

idt_wass(
  x1,
  x2 = NULL,
  stat = FALSE,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  incr = 0.5,
  perm = FALSE,
  n_perm = 10^5
)

## S3 method for class 'numeric'
idt_wass(
  x1,
  x2 = NULL,
  stat = FALSE,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  incr = 0.5,
  perm = FALSE,
  n_perm = 10^5
)

## S3 method for class 'list'
idt_wass(
  x1,
  x2 = NULL,
  stat = FALSE,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  incr = 0.5,
  perm = FALSE,
  n_perm = 10^5
)

Arguments

Value

For two vectors x1 and x2, the probability that Monte Carlo permutation of samples results in a lower empirical scaled Wassertein R1 distance than the one obtained. For a list of vectors input in x1, a matrix of probabilities pairwise between all vectors.

Description

This function computes the Kolmogorov-Smirnov (KS) distance between two empirical cumulative distribution functions. For more functionality, use ks.test.

Usage

ks_arkhaia(x1, x2 = NULL)

## S3 method for class 'numeric'
ks_arkhaia(x1, x2 = NULL)

## S3 method for class 'list'
ks_arkhaia(x1, x2 = NULL)

Arguments

Details

The Rcpp-based function ks_arkhaia is used for faster estimation of the KS distance than ks.test.

Value

The KS distance between the two vectors.

Description

For a contingency table with columns representing contexts and rows representing types, computes the log odds ratio of a 2 x 2 contingency table of the presence-absences across each pair of columns. The addition of 0.5 to cells of the contingency table is performed (Anscombe 1956; Haldane 1956).

Usage

log_OR_pair(x)

## S3 method for class 'matrix'
log_OR_pair(x)

## S3 method for class 'data.frame'
log_OR_pair(x)

## S3 method for class 'xtabs'
log_OR_pair(x)

## S3 method for class 'table'
log_OR_pair(x)

Arguments

Value

A matrix giving the log odds ratio between all columns of the input.

Examples

x1 <- c(2, 0, 0, 11, 5, 0, 2, 0, 4)
x2 <- c(1, 1, 0, 23, 3, 3, 0, 0, 0)
x3 <- c(1, 0, 0, 0, 10, 0, 4, 0, 1)

x <- data.frame(S1 = x1, S2 = x2, S3 = x3)
rownames(x) <- LETTERS[1:nrow(x)]

log_OR_pair(x)

Description

Performs a simple least squares fitting to time indexed data of the form $x(t) = \beta_{0} + \sum_{i =1}^n \beta_{1i} \cos (2 \pi f t) + \beta_{2i} \sin(2 \pi f t)$, using a range of potential frequencies (Vaníček 1969, 1971). Intercept may be ommitted.

Usage

LSSA(
  x,
  freqs = seq(0.001, 0.5, by = 5e-04),
  intercept = TRUE,
  type = "frequency"
)

## S3 method for class 'time_series'
LSSA(
  x,
  freqs = seq(0.001, 0.5, by = 5e-04),
  intercept = TRUE,
  type = "frequency"
)

Arguments

Value

A data frame containing the power and residual sum of squares for each frequency, as well as coefficients.

References

Vaníček P (1969). “Approximate Spectral Analysis by Least-Squares Fit.” Astrophysics and Space Science, 4, 387–391. doi:10.1007/BF00651344.

Vaníček P (1971). “Further development and properties of the spectral analysis by least-squares fit.” Astrophysics and Space Science, 12, 10–33. doi:10.1007/BF00656134.

Examples

t_ <- runif(100, 0, 100)
y <- 5 * sin(0.1 * t_) - 2.3 * cos(0.3 * t_ + 1)
dat <- time_series(t = t_, x = y)
LSSA(dat)

Description

Performs a simple least squares fitting to time indexed data of the form $x(t) = \beta_{0} + \sum_{i =1}^n \beta_{1i} \cos (2 \pi f t) + \beta_{2i} \sin(2 \pi f t)$, using an input of frequencies; the lowest frequency peak (not the highest power frequency) is chosen for regression, up to a chosen number of iterations. Intercept may be ommitted. The lowest frequency is equivalent to the longest period.

Usage

LSSA_LFI(x, n_iter = 1, intercept = TRUE, AIC = FALSE)

## S3 method for class 'time_series'
LSSA_LFI(x, n_iter = 1, intercept = TRUE, AIC = FALSE)

Arguments

Value

A list containing:

• A list of the coefficients for each iteration (the intercept is included in the first iteration).

• A vector of the frequencies.

• The residual sum of squares (RSS) after each iteration (decreasing).

• The AIC upon each iteration. (If the parameter AIC is TRUE, this will stop at the lowest AIC value produced by the frequencies tested).

References

Akaike H (1973). “Information Theory and an Extension of the Maximum Likelihood Principle.” In Petrov BN, Caski F (eds.), Proceeding of the Second International Symposium on Information Theory, 267–281. Akademiai Kiado, Budapest.

Description

For a set of time series (namely partitions of set of series) contained in a list, will compute the Akaike Information Criterion (AIC) for each candidate set (Akaike 1973).

Usage

LSSA_LFI_candidates(x, sets = NULL, n_iter = 1, intercept = TRUE)

## S3 method for class 'time_series'
LSSA_LFI_candidates(x, sets = NULL, n_iter = 1, intercept = TRUE)

Arguments

Value

The index of the set yielding the lowest AIC. If sets is NULL, the output of [1] indicates linear dependence; if the output is [2], linear independence.

References

Akaike H (1973). “Information Theory and an Extension of the Maximum Likelihood Principle.” In Petrov BN, Caski F (eds.), Proceeding of the Second International Symposium on Information Theory, 267–281. Akademiai Kiado, Budapest.

Description

For multiple time series contained in a list, this function will compute the Akaike Information Criterion (AIC) for the best-fitting models particular to each series, including the case of an intercept-only model. This function can be performed after LSSA_LFI_candidates and repartition to determine the appropriate number of terms. For the situation where all time series must have the same number of terms, LSSA_LFI_multi should be used, but this function should chosose a better fitting model, since it adjusts the number of parameters for each dataset.

Usage

LSSA_LFI_comp(x, intercept = TRUE)

## S3 method for class 'time_series'
LSSA_LFI_comp(x, intercept = TRUE)

Arguments

Value

A list giving the number of parameters (k) and residual sum of squares (rss) for each dataset in x, along with the AIC for the paritioned model.

Description

Evaluate pairwise linear dependence between two time series using a LSSA-LFI valdiated model selection (see LSSA_LFI_validated)), with variable length time period.

Usage

LSSA_LFI_epoch(
  x,
  pair = NULL,
  n_iter = 1,
  intercept = TRUE,
  t_range = NULL,
  h_range = NULL,
  t_grid = 1,
  h_grid = 1
)

## S3 method for class 'list'
LSSA_LFI_epoch(
  x,
  pair = NULL,
  n_iter = 1,
  intercept = TRUE,
  t_range = NULL,
  h_range = NULL,
  t_grid = 1,
  h_grid = 1
)

Arguments

Value

A matrix giving the probability of linear dependence, predicated upon time $t$ and window length $h$.

Description

Generates a data frame of values $x(t)$ of the model generated by LSSA-LFI (see LSSA_LFI).

Usage

LSSA_LFI_model(x, t_ = NULL, n_iter = 1, intercept = TRUE, label = "model")

## S3 method for class 'time_series'
LSSA_LFI_model(x, t_ = NULL, n_iter = 1, intercept = TRUE, label = "model")

Arguments

Value

A data frame containing $t, x(t)$.

Description

For multiple time series contained in a time_series object, this function will compute the Akaike Information Criterion (AIC) as the number of terms (n_iter) is increased. This function can be performed after LSSA_LFI_candidates and repartition to determine the appropriate number of terms.

Usage

LSSA_LFI_multi(x, n_iter = 1, intercept = TRUE, AIC = FALSE)

## S3 method for class 'time_series'
LSSA_LFI_multi(x, n_iter = 1, intercept = TRUE, AIC = FALSE)

Arguments

Value

A data frame giving the number of iterations and the AIC for each.

References

Akaike H (1973). “Information Theory and an Extension of the Maximum Likelihood Principle.” In Petrov BN, Caski F (eds.), Proceeding of the Second International Symposium on Information Theory, 267–281. Akademiai Kiado, Budapest.

Description

Evaluate pairwise linear dependence between observations using a LSSA-LFI validated model selection (see LSSA_LFI_validated).

Usage

LSSA_LFI_pairwise(x, n_iter = 1, intercept = TRUE)

## S3 method for class 'time_series'
LSSA_LFI_pairwise(x, n_iter = 1, intercept = TRUE)

Arguments

Value

An upper-triangular matrix, containing the probability of linear dependence between series.

Description

Probability of linear dependence between two groups of time series observations using a LSSA-LFI model selection (see LSSA_LFI_candidates), on the basis of the inclusion of a third "attendant" variate. The third attendant variate is selected from the remaining time series in the list, hence the input list must include at least three times series.

Usage

LSSA_LFI_validated(x, pair = NULL, n_iter = 1, intercept = TRUE)

## S3 method for class 'time_series'
LSSA_LFI_validated(x, pair = NULL, n_iter = 1, intercept = TRUE)

Arguments

Value

The probability of linear dependence between two time series, in which 1 indicates linear dependence almost surely and 0 indicates independence.

Description

Create a 2 x 2 contingency table of the presence/absence of a given type

Usage

pa_matrix(x)

## S3 method for class 'matrix'
pa_matrix(x)

## S3 method for class 'data.frame'
pa_matrix(x)

## S3 method for class 'table'
pa_matrix(x)

## S3 method for class 'xtabs'
pa_matrix(x)

Arguments

Value

A 2 x 2 contingency table of the counts of types present in both, either, or neither context.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)

x <- data.frame(S1 = x1, S2 = x2)
rownames(x) <- LETTERS[1:5]

pa_matrix(x)

Description

For a matrix of cross-tabulated counts of observations which constitute a minimum threshold, this function esimates the rate parameter column-wise, either retaining or omitting zeros, by a least-squares approach.

Usage

pois_rcens(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'matrix'
pois_rcens(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'data.frame'
pois_rcens(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'xtabs'
pois_rcens(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'table'
pois_rcens(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

Arguments

Value

A vector of the rate parameters for each column.

Examples

x1 <- c(1,2,2,5,7,0,0)
x2 <- c(9,2,5,15,7,90,0)
x <- matrix(c(x1,x2), ncol = 2)

pois_rcens(x)
pois_rcens(x, omit_zero = FALSE)

Description

Given multiple time series in a time_series object (x), group the variates into a new set of variates, expressed as a list of the variate names (set). Returns a time_series object using the new partitioning of variates.

Usage

repartition(x, set = NULL)

## S3 method for class 'time_series'
repartition(x, set = NULL)

Arguments

Value

A list containing the data according to the partition structure described by set.

Examples

idx <- runif(40, 0, 100)
x1 <- runif(10, 0, 1) + 3
x2 <- runif(10, 0, 1) + 2
x3 <- runif(10, 0, 1) + 1
x4 <- runif(10, 0, 1)
x <- time_series(t = idx, x = c(x1,x2,x3,x4),
  variate = c(rep("x1", 10), rep("x2", 10), 
  rep("x3", 10), rep("x4", 10)))

repartition(x, set = list(c("x1", "x4"), "x2", "x3"))

Description

For two one-dimensional temporal point processes $X_1$ and $X_2$, this function estimates the condition of the two processes becoming "integrated in distribution over time" (i.d.t.) at a moment in time $t$. This is achieved by computing the Kolmogorov-Smirnov distance $D$ between their empirical culumative distribution functions (e.c.d.f.), before and after $t$ for some duration $h$, and taking the difference between the distances $\theta = D_{before}$ - $D_{after}$. For practical significance in the estimation of $\theta$, Monte Carlo permutation of samples is used to estimate the probability that the observed value of $\theta$ is greater than the distribution of permuted samples (i.e., that observations are interchangable between $X_1$ and $X_2$).

Usage

th_idt_ks(
  x1,
  x2 = NULL,
  stat = FALSE,
  incr = 0.5,
  perm = FALSE,
  n_perm = 1e+05
)

## S3 method for class 'numeric'
th_idt_ks(
  x1,
  x2 = NULL,
  stat = FALSE,
  incr = 0.5,
  perm = FALSE,
  n_perm = 1e+05
)

## S3 method for class 'list'
th_idt_ks(
  x1,
  x2 = NULL,
  stat = FALSE,
  incr = 0.5,
  perm = FALSE,
  n_perm = 1e+06
)

Arguments

Value

A list containing a data frame two vectors x1 and x2, the probability that Monte Carlo permutation of samples results in a lower distance than the one obtained. For a list of vectors input in x1, a matrix of probabilities pairwise between all vectors.

Description

For two one-dimensional point processes, this function estimates the condition of the two processes becoming i.d.t. at a moment of time $t$ considering a window of time around that moment, $(t-h,t+h)$. This is achieved by computing the difference of the empirical scaled Wasserstein R1 distances between the two processes before and after $t$. Monte Carlo permutation of samples is used to estimate the probability that the obtain distances is of practical signficance.

Usage

th_idt_wass(
  x1,
  x2 = NULL,
  stat = FALSE,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  incr = 0.5,
  perm = FALSE,
  n_perm = 10^5
)

## S3 method for class 'numeric'
th_idt_wass(
  x1,
  x2 = NULL,
  stat = FALSE,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  incr = 0.5,
  perm = FALSE,
  n_perm = 10^5
)

## S3 method for class 'list'
th_idt_wass(
  x1,
  x2 = NULL,
  stat = FALSE,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  incr = 0.5,
  perm = FALSE,
  n_perm = 10^5
)

Arguments

Value

For two vectors x1 and x2, the probability that Monte Carlo permutation of samples results in a lower empirical scaled Wassertein R1 distance than the one obtained. For a list of vectors input in x1, a matrix of probabilities pairwise between all vectors.

Description

Creates an object of class time_series from a matrix or data frame, or by giving a filename for a csv file in the working directory. The first column contains time indices (t), the second the value of observations (x), both of which must be numeric, and the third contains a label as a factor column (variate). Multiple time series are contained in the same time_series object, distinguished by different labels.

Usage

time_series(
  input,
  t = NULL,
  x = NULL,
  variate = NULL,
  log = FALSE,
  inverse = FALSE,
  standard = FALSE,
  ...
)

## S3 method for class 'matrix'
time_series(
  input,
  t = NULL,
  x = NULL,
  variate = NULL,
  log = FALSE,
  inverse = FALSE,
  standard = FALSE,
  ...
)

## S3 method for class 'data.frame'
time_series(
  input,
  t = NULL,
  x = NULL,
  variate = NULL,
  log = FALSE,
  inverse = FALSE,
  standard = FALSE,
  ...
)

## S3 method for class 'character'
time_series(
  input,
  t = NULL,
  x = NULL,
  variate = NULL,
  log = FALSE,
  inverse = FALSE,
  standard = FALSE,
  ...
)

## S3 method for class 'numeric'
time_series(
  input = NULL,
  t = NULL,
  x = NULL,
  variate = NULL,
  log = FALSE,
  inverse = FALSE,
  standard = FALSE,
  ...
)

Arguments

Value

A time_series object.

Examples

idx <- runif(100,0,100)
x <- cumsum(rnorm(100,0,1))
label <- rep("x", 100)
mat <- matrix(c(idx, x, label), ncol = 3)
time_series(mat)

dat <- data.frame(idx, x, label)
time_series(dat)

time_series(t = idx, x = x, variate = label)

Description

For a contingency table with columns representing contexts and rows representing types, computes the trace of a 2 x 2 contingency table of the presence-absences across each pair of columns.

Usage

trace_pair(x)

## S3 method for class 'matrix'
trace_pair(x)

## S3 method for class 'data.frame'
trace_pair(x)

## S3 method for class 'xtabs'
trace_pair(x)

## S3 method for class 'table'
trace_pair(x)

Arguments

Value

A matrix giving the trace between all columns of the input.

Examples

x1 <- c(2, 0, 0, 11, 5, 0, 2, 0, 4)
x2 <- c(1, 1, 0, 23, 3, 3, 1, 1, 1)
x3 <- c(1, 0, 0, 0, 10, 0, 4, 0, 0)

x <- data.frame(S1 = x1, S2 = x2, S3 = x3)
rownames(x) <- LETTERS[1:nrow(x)]

trace_pair(x)

Description

For a data frame in which the first column contains a time index and the second colum observations, trim the data frame to include observations only with a given epoch (time period).

Usage

trim_epoch(x, epoch = NULL)

## S3 method for class 'time_series'
trim_epoch(x, epoch = NULL)

Arguments

Value

A data frame containing only those observations with time indices within the epoch.

Description

For a matrix of cross-tabulated counts of observations which constitute a minimum threshold, returns a contingency table whose counts are sampled according to a truncated Poisson distribution, whose rate parameter is determined column-wise (see pois_rcens).

Usage

trunc_pois(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'matrix'
trunc_pois(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'data.frame'
trunc_pois(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'xtabs'
trunc_pois(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

## S3 method for class 'table'
trunc_pois(x, lambda_grid = seq(0.01, 100, by = 0.01), omit_zero = TRUE)

Arguments

Value

A contingency table $Y$ of the same size as $X$, with $y_{ij}$ drawn according to a truncated Poisson distribution that ensures $y_{ij} \geq x_{ij}$.

Examples

x1 <- c(1,2,2,5,7,0,0)
x2 <- c(9,2,5,15,7,90,0)
x <- matrix(c(x1,x2), ncol = 2)

pois_rcens(x)
pois_rcens(x, omit_zero = FALSE)

Description

For a matrix of cross-tabulated counts of observations, estimates Cramer's V using Bergsma's bias correction (Bergsma 2013), using the Cressie-Read power divergence statistic (see CR).

Usage

VB(x, lambda = 2/3)

## S3 method for class 'matrix'
VB(x, lambda = 2/3)

## S3 method for class 'data.frame'
VB(x, lambda = 2/3)

## S3 method for class 'xtabs'
VB(x, lambda = 2/3)

## S3 method for class 'table'
VB(x, lambda = 2/3)

Arguments

Value

Bergsma's bias-corrected etimate of Cramer's $V$.

References

Bergsma W (2013). “A Bias-Correction for Cramér’s $V$ and Tschuprow’s $T$.” Journal of the Korean Statistical Society, 42, 323–328. doi:10.1016/j.jkss.2012.10.002.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)
x3 <- c(0, 0, 2, 81, 11)

x <- matrix(c(x1, x2, x3), ncol = 3)

VB_pair(x)
VB(x, lambda = 1)

Description

To evaluate the stability of estimates of effect sizes between archaeological contexts in light of the inclusion or exclusion of a given type, this routine computes bias-corrected Cramer's V VB) omitting a type on each iteration.

Usage

VB_LOO_type(x, lambda = 2/3)

## S3 method for class 'matrix'
VB_LOO_type(x, lambda = 2/3)

## S3 method for class 'data.frame'
VB_LOO_type(x, lambda = 2/3)

## S3 method for class 'xtabs'
VB_LOO_type(x, lambda = 2/3)

## S3 method for class 'table'
VB_LOO_type(x, lambda = 2/3)

Arguments

Value

A three-dimensional array of the pairwise context-by-context effect sizes given the ommission of a type, for all types given in the input data frame.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)
x3 <- c(0, 0, 2, 81, 11)

x <- matrix(c(x1, x2, x3), ncol = 3)

rownames(x) <- LETTERS[1:nrow(x)]
colnames(x) <- c("S1", "S2", "S3")

VB_LOO_type(x)

Description

For a matrix or data frame of cross-tabulated counts of observations, estimates Cramer's V using Bergsma's bias correction (Bergsma 2013) by subsetting the table by pairs of columns (see VB). In subsetting, zero row/columns are automatically removed from the subset matrix.

Usage

VB_pair(x, lambda = 2/3)

## S3 method for class 'matrix'
VB_pair(x, lambda = 2/3)

## S3 method for class 'data.frame'
VB_pair(x, lambda = 2/3)

## S3 method for class 'xtabs'
VB_pair(x, lambda = 2/3)

## S3 method for class 'table'
VB_pair(x, lambda = 2/3)

Arguments

Value

A matrix of Bergsma's bias-corrected etimate of Cramer's $V$, pairwise between columns of the input matrix, of class effect_sizes.

References

Bergsma W (2013). “A Bias-Correction for Cramér’s $V$ and Tschuprow’s $T$.” Journal of the Korean Statistical Society, 42, 323–328. doi:10.1016/j.jkss.2012.10.002.

Examples

x1 <- c(2, 0, 10, 11, 5)
x2 <- c(1, 1, 17, 23, 3)
x3 <- c(0, 0, 2, 81, 11)

x <- matrix(c(x1, x2, x3), ncol = 3)

VB_pair(x)
VB_pair(x, lambda = 1)

Description

Given a matrix of cross-tabulated counts of observations which constitute a minimum threshold, returns the distribution of bias-corrected Cramer's $V$ by resampling from a truncated Poisson distribution, with rates determined column-wise (see VB, trunc_pois).

Usage

VB_trunc_pois(
  x,
  lambda = 2/3,
  lambda_grid = seq(0.01, 100, by = 0.01),
  omit_zero = TRUE,
  n_iter = 10^5
)

## S3 method for class 'matrix'
VB_trunc_pois(
  x,
  lambda = 2/3,
  lambda_grid = seq(0.01, 100, by = 0.01),
  omit_zero = TRUE,
  n_iter = 10^5
)

## S3 method for class 'data.frame'
VB_trunc_pois(
  x,
  lambda = 2/3,
  lambda_grid = seq(0.01, 100, by = 0.01),
  omit_zero = TRUE,
  n_iter = 10^5
)

## S3 method for class 'xtabs'
VB_trunc_pois(
  x,
  lambda = 2/3,
  lambda_grid = seq(0.01, 100, by = 0.01),
  omit_zero = TRUE,
  n_iter = 10^5
)

## S3 method for class 'table'
VB_trunc_pois(
  x,
  lambda = 2/3,
  lambda_grid = seq(0.01, 100, by = 0.01),
  omit_zero = TRUE,
  n_iter = 10^5
)

Arguments

Value

A contingency table $Y$ of the same size as $X$, with $y_{ij}$ drawn according to a truncated Poisson distribution, $y_{ij} \geq x_{ij}$.

Examples

x1 <- c(1,2,2,5,7,0,0)
x2 <- c(9,2,5,15,7,90,0)
x <- matrix(c(x1,x2), ncol = 2)

VB_trunc_pois(x, n_iter = 10^2)
VB_trunc_pois(x, omit_zero = FALSE, n_iter = 10^2)

Description

For two or more one-dimensional point processes, computes their Wasserstein distance via their empirical cumuluative density functions (e.c.d.f.), adjusting for sample size and the scale of their durations (Vasershtein 1969; Anderson 1962; Ramdas et al. 2017), using numerical quadrature:

$\displaystyle{W_{1s} = \frac{1}{s} \int_\mathbf{R} \vert F_1(x) - F_2(x) \vert \, dx}$

where $s$ is a scaling coefficient, namely either the range of the point process or its support. More than two processes result in pairwise estimation of processes.

Usage

wass_R1(
  x1,
  x2 = NULL,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  perm = FALSE,
  n_perm = 10^5
)

## S3 method for class 'numeric'
wass_R1(
  x1,
  x2 = NULL,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  perm = FALSE,
  n_perm = 10^5
)

## S3 method for class 'list'
wass_R1(
  x1,
  x2 = NULL,
  scaled = FALSE,
  scaled_by = 0,
  quad_by = 0.001,
  perm = FALSE,
  n_perm = 10^5
)

Arguments

Value

For two vectors x1 and x2, the empirical scaled Wassertein R1 distance between the two e.c.d.f. of their samples. For a list of vectors input in x1, a matrix of the empirical scaled Wasserstein R1 distances pairwise between all vectors.

References

Anderson TW (1962). “On the Distribution of the Two-Sample Cramer–von Mises Criterion.” Annals of Mathematical Statistics, 33, 1148–1159. doi:10.1214/aoms/1177704477.

Ramdas A, García Trillos N, Cuturi M (2017). “On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests.” Entropy, 19.47, 1–15. doi:10.3390/e19020047.

Vasershtein LN (1969). “Markov processes over denumerable products of spaces, describing large systems of automata.” Problemy Peredači Informacii, 5, 64–72.