Package 'arkhaia'

Cressie-Read Power-Divergence Statistic

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

x	A matrix of cross-tabulated counts.
lambda	The parameter of the Cressie-Read power-divergence statistic. Default is the recommended value of 2/3. To use Pearson's method, set lambda = 1.

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)

---

Homogeneity of Related Assemblages via Effect Size

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

x	An effect_sizes object as returned by VB_pair.
related	The related pairs of contexts as a two-column matrix or data frame (contexts between which one anticipates a meaningful relationship). Names must match colnames(x).
unrelated	The unrelated pairs of contexts as a two-column matrix or data frame (contexts between which one does not anticipate a meaningful relationship). Names must match colnames(x). May be left NULL, in which event all pairs not expressed in related are created
direction	Whether the related or unrelated effect size should come first. Default is "UW"; alternative is "WU".

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)

---

Leave-One-Out Routine for Homogeneity of Related Assemblages

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

x	A data frame or matrix representing a contingency table of counts, with contexts along the columns and types along rows.
related	The related pairs of contexts as a two-column matrix or data frame (contexts between which one anticipates a meaningful relationship). Names must match colnames(x).
unrelated	The unrelated pairs of contexts as a two-column matrix or data frame (contexts between which one does not anticipate a meaningful relationship). Names must match colnames(x).
direction	Whether the related or unrelated effect size should come first. Default is "UW"; alternative is "WU".
lambda	Parameter of the Cressie-Read power-divergence statistic. Default is the recommended value of 2/3.

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)

---

Log Odds Ratio with Haldane-Anscombe's Correction Pairwise between Columns

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

x	A matrix or data frame with contexts along columns and types along rows.

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)

---

Least Squares Spectral Analysis (LSSA)

Description

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

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

Arguments

x	A data frame of two columns, the first containing time indices and the second containing values.
freqs	A vector of frequencies to evaluate. By default a grid from 0.001 to 0.5 is tested at an interval of 0.005.
intercept	Whether to include the intercept. Default is TRUE.
type	Type of output. Can be either "frequency" (the default) or "period".

Value

The 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.

---

Least Squares Spectral Analysis via Lowest Frequency Iteration (LSSA-LFI)

Description

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

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

Arguments

x	A data frame of two columns, with the first column containing time indices and the second containing values.
n_iter	The number of iterations to run. Default is 1.
intercept	Whether to include the intercept. Default is TRUE.
AIC	If TRUE, only the result that has yeilded the lowest AIC is given (Akaike 1973). Default is FALSE.

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.

---

Linear Dependence of LSSA-LFI Candidate Models via AIC

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

Arguments

x	A list containing the time series, each of which should be a matrix or data frame with time index in the first column and value in the second.
sets	Candidate sets to evaluate; must be a list of lists containing the indices of the sets in x. If left NULL, two sets are evaluated: all series pooled together [1] and all series kept separate [2].
n_iter	The number of iterations to run for the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is 1.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.

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.

---

Partitioned LSSA-LFI Model Terms and AIC: Composite Number of Parameters

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 'list'
LSSA_LFI_comp(x, intercept = TRUE)

Arguments

x	A list containing the time series, each of which should be a matrix or data frame with time index in the first column and value in the second.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.

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.

---

Period-Variable Pairwise Selection of Linearly Dependent LSSA-LFI Models

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

x	A list of data frames.
pair	The pair of commodities to evaluate in the list x, given as indices.
n_iter	The number of iterations to run. Default is 1.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.
t_range	The range of the time period. Default are the minimum and maximum dates spanned by the data in x.
h_range	The range of the potential windows of $h$. Default is from 0 to entire span of t_range.
t_grid	The length of interval along which to sample $t$. Default is 1.
h_grid	The length of interval along which to sample $h$. Default is 1.

Value

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

---

LSSA-LFI Model

Description

Generates a data frame of values $f(t)$ 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 'matrix'
LSSA_LFI_model(x, t_ = NULL, n_iter = 1, intercept = TRUE, label = "model")

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

Arguments

x	A data frame where time indices are in the first column and values are in the second.
t_	A vector giving samples range of $t$ for computing $f(t)$. Default is from the minimum to maximum time index sampled at 0.01 intervals.
n_iter	The number of iterations to run. Default is 1.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.
label	Default is "model".

Value

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

---

Partitioned LSSA-LFI Model Terms and AIC

Description

For multiple time series contained in a list, 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 'list'
LSSA_LFI_multi(x, n_iter = 1, intercept = TRUE, AIC = FALSE)

Arguments

x	A list containing the time series, each of which should be a matrix or data frame with time index in the first column and value in the second.
n_iter	The number of iterations to run for the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is 1.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.
AIC	If TRUE, only the result that has yeilded the lowest AIC is given (Akaike 1973). Default is FALSE.

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.

---

Pairwise Selection of Linearly Dependent LSSA-LFI Models

Description

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

Usage

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

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

Arguments

x	A list of data frames.
n_iter	The number of iterations to run. Default is 1.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.

Value

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

---

Validated Linear Dependence via LSSA-LFI

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

Arguments

x	A list of data frames.
pair	The pair of series to evaluate in the list x, given as indices.
n_iter	The number of iterations to run. Default is 1.
intercept	Whether to include the intercept in the least squares spectral analysis via lowest frequency iteration (LSSA-LFI). Default is TRUE.

Value

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

---

Presence-Absence Matrix

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

x	A matrix or data frame where the two columns indicate contexts and the rows indicate types, with each cell containing counts of types in a context.

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)

---

Least Squares Fit of Poisson Distribution for Random Right-Censored Data

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

x	A matrix of cross-tabulated counts.
lambda_grid	The resolutation at which to sample for the rate parameter. Default is seq(0.1, 100, by = 0.01).
omit_zero	Whether to omit zeros. Default is TRUE.

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)

---

Repartition (Group) Datasets

Description

Given a list of data frames (or matrices), labeled x, and another list which contains indices of x as vectors, labeled set, returns a new list which pools (row-binds) the data frames together according to the grouprings in set.

Usage

repartition(x, set = NULL)

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

Arguments

x	A list containing the time series, each of which should be a matrix or data frame with time index in the first column and value in the second.
set	A list of vectors containing the indices of the sets in x, according to which to pool the datasets into a new list.

Value

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

---

Trace Coefficient Pairwise between Columns

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

x	A matrix or data frame with contexts along columns and types along rows.

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)

---

Trim to Epoch

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 'matrix'
trim_epoch(x, epoch = NULL)

## S3 method for class 'data.frame'
trim_epoch(x, epoch = NULL)

Arguments

x	A data frame or matrix containing time-indexed data, with time index in the first column and value in the second.
epoch	A numeric vector given the start and end time indices of the epoch.

Value

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

---

Resampled Contingency Table via a Truncated Poisson for Random Right-Censored Data

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

x	A matrix of cross-tabulated counts.
lambda_grid	The resolutation at which to sample for the rate parameter. Default is seq(0.1, 100, by = 0.01).
omit_zero	Whether to omit zeros. Default is TRUE.

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)

---

Bias-Corrected Cramer's V

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

x	A matrix or data frame of cross-tabulated counts.
lambda	Parameter of the Cressie-Read power-divergence statistic. Default is the recommended value of 2/3.

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)

---

Leave-One-Out Type Routine for Pairwise Effect Sizes of Archaeological Contexts

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

x	A contingency table as a matrix or data frame expressing counts, with contexts along columns and types along rows.
lambda	Parameter of the Cressie-Read power-divergence statistic. Default is the recommended value of 2/3.

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)

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Bias-Corrected Cramer's V Pairwise between Columns

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

x	A matrix or data frame of cross-tabulated counts.
lambda	Parameter of the Cressie-Read power-divergence statistic. Default is the recommended value of 2/3.

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)

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Bias-Corrected Cramer's V for Random Right-Censored Data

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

x	A matrix of cross-tabulated counts.
lambda	The value of lambda (default is 2/3) for the Cressie-Read power divergence statistic used to estimate the bias-corrected Cramer's $V$. Default is 2/3.
lambda_grid	The resolutation at which to sample for the rate parameter. Default is seq(0.1, 100, by = 0.01).
omit_zero	Whether to omit zeros. Default is TRUE.
n_iter	Number of samples of $V$ to take. Default is 10^5.

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)

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