compute_iota2 {iotarelr}

Computes Iota and its elements in version 2

Description

Fits a model of Iota2 to the data

Usage

compute_iota2(
  data,
  random_starts = 10,
  max_iterations = 5000,
  cr_rel_change = 1e-12,
  con_step_size = 1e-04,
  con_rel_convergence = 1e-12,
  con_max_iterations = 5000,
  con_random_starts = 5,
  b_min = 0.01,
  fast = TRUE,
  trace = TRUE,
  con_trace = FALSE
)

Arguments

data

Data for which the elements should be estimated. Data must be an object of type data.frame or matrix with cases in the rows and raters in the columns.

random_starts

An integer for the number of random starts for the EM algorithm.

max_iterations

An integer for the maximum number of iterations within the EM algorithm.

cr_rel_change

Positive numeric value for defining the convergence of the EM algorithm.

con_step_size

Double for specifying the size for increasing or decreasing the probabilities during the conditioning stage of estimation. This value should not be less than 1e-3.

con_rel_convergence

Double for determining the convergence criterion during the conditioning stage. The algorithm stops if the relative change is smaller than this criterion.

con_max_iterations

Integer for the maximum number of iterations during the conditioning stage.

con_random_starts

Integer for the number of random starts within the conditioning stage.

b_min

Value ranging between 0 and 1, determining the minimal size of the categories for checking if boundary values occurred. The algorithm tries to select solutions that are not considered to be boundary values.

fast

Bool If TRUE a fast estimation is applied during the condition stage. This option ignores all parameters beginning with "con_". If FALSE the estimation described in Berding and Pargmann (2022) is used. Default is TRUE.

trace

TRUE for printing progress information on the console. FALSE if this information is not to be printed.

con_trace

TRUE for printing progress information on the console during estimations in the conditioning stage. FALSE if this information is not to be printed.

Value

Returns a list with the following three components: The first component estimates_categorical_level comprises all elements that describe the ratings on a categorical level. The elements are sub-divided into raw estimates and chance-corrected estimates.

raw_estimates

alpha_reliability:

A vector containing the Alpha Reliabilities for each category. These values represent probabilities.

beta_reliability:

A vector containing the Beta Reliabilities for each category. These values represent probabilities.

assignment_error_matrix:

Assignment Error Matrix containing the conditional probabilities for assigning a unit of category i to categories 1 to n.

iota:

A vector containing the Iota values for each category.

iota_error_1:

A vector containing the Iota Error Type I values for each category.

iota_error_2:

A vector containing the Iota Error Type II values for each category.

elements_chance_corrected

alpha_reliability:

A vector containing the chance-corrected Alpha Reliabilities for each category.

beta_reliability:

A vector containing the chance-corrected Beta Reliabilities for each category.

The second component estimates_scale_level contains elements for describing the quality of the ratings on a scale level. It comprises the following elements:

iota_index:

The Iota Index, representing the reliability on a scale level.

iota_index_d4:

The Static Iota Index, which is a transformation of the original Iota Index, in order to consider the uncertainty of estimation.

iota_index_dyn2:

The Dynamic Iota Index, which is a transformation of the original Iota Index, in order to consider the uncertainty of estimation.

The third component information contains important information regarding the parameter estimation. It comprises the following elements:

log_likelihood:

Log-likelihood of the best solution.

convergence:

If estimation converged 0, otherwise 1.

est_true_cat_sizes:

Estimated categorical sizes. This is the estimated amount of the categories.

conformity:

0 if the solution is in line with assumptions of weak superiority. A number greater 0 indicates the number of violations of the assumption of weak superiority.

random_starts:

Numer of random starts for the EM algorithm.

boundaries:

False if the best solution does not contain boundary values. True if the best solution does contain boundary values

p_boundaries:

Percentage of solutions with boundary values during the estimation.

call:

Name of the function that created the object.

n_rater:

Number of raters.

n_cunits:

Number of coding units.

References

Florian Berding and Julia Pargmann (2022).Iota Reliability Concept of the Second Generation. Measures for Content Analysis Done by Humans or Artificial Intelligences. Berlin: Logos. https://doi.org/10.30819/5581