# Fit Models to Two-Way Tables with Correlated Ordered Response Categories

## Documentation for package ‘ordinalTables’ version 1.0.0.3

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

A B C D E F G H I K L M N O P R S T U V W

## -- A --

Agresti_bisection | Solves equation Agresti_f() = 0 for delta by method of bisection..
Agresti_compute_lambda | Computes value of lambda parameter
Agresti_compute_pi | Computes the matrix pi of model-based proportions
Agresti_create_design_matrix | Creates the design matrix for Agresti's simple diagonal quasi-symmetry model.
Agresti_equation_1 | First equation in section 3. Solved for kappa.
Agresti_equation_2 | Second equation in section 3. Solved for pi_margin.
Agresti_equation_3 | Third equation in section 3. Solved for lambda
Agresti_extract_delta | Extracts the quasi-symmetry information from the result provided.
Agresti_f | Function value for first equation in section 3.
Agresti_kappa_agreement | Fits Agresti's agreement model that includes kappa as a parameter.
Agresti_simple_diagonals_parameter_quasi_symmetry | Agresti's simple diganal quasi-symmetry model.
Agresti_starting_values | Computes staring values for marginal pi.
Agresti_weighted_tau | Computes weighted tau from Section 2.1. Agresti, A. (1983). Testing marginal homogeneity for ordinal categorical variables. Biometrics, 39(2), 505-510.
Agresti_w_diff | Computes the weighted statistics listed in section 2.3.

## -- B --

Bhapkar_marginal_homogeneity | Bhapkar's (1979) test for marginal homogeneity
Bhapkar_quasi_symmetry | Bhapkar's 1979 test for quasi-symmetry.
Bowker_symmetry | Computes Bowker's test of symmetry.
budget_actual | Participation in household budgeting by psychiatric patients. Rows are ratings by patient, columns are ratings by relative. 1 - not at all 2 - doing some 3 - doing regularly
budget_expected | Ratings of expected participation in household budgeting by psychiatric patients. Rows are ratings by patient, columns are ratings by relative. 1 - not at all 2 - doing some 3 - doing regularly

## -- C --

Clayton_marginal_location | Fits the tests comparing locations of the margins of a two-way table.
Clayton_stratified_marginal_location | Clayton's stratified version of the marginal location comparison.
Clayton_summarize | Computes summary, cumulative proportions up to index provided
Clayton_summarize_stratified | Analysis stratified by column variable j.
Clayton_two_way_association | Clayton's stratified measure of association
Cliff_as_d_matrix | Converts two vectors containing scores and integer frequencies (cell counts) into a d-matrix
Cliff_compute_d | Computes between groups dominance matrix "d".
Cliff_counts_2 | Generates counts from table frequencies for 2 category items
Cliff_counts_3 | Generates counts from table frequencies for 3 category items
Cliff_counts_4 | Generates counts from table frequencies for 4 category items
Cliff_counts_5 | Generates counts from table frequencies for 5 category items
Cliff_counts_6 | Generates counts from table frequencies for 6 category items
Cliff_dependent | Computes Cliff's dependent d-statistics based on a dominance matrix.
Cliff_dependent_compute_cov | Computes sum term in covariance db-dw for weighted dominance matrix.
Cliff_dependent_compute_cov_from_d | Compute the sum in the covariance of db+dw
Cliff_dependent_compute_from_matrix | Computes Cliff's dependent d-statistics based on a dominance matrix.
Cliff_dependent_compute_from_table | Computes Cliff's dependent d-statistics based on a table of frequency counts.
Cliff_dependent_compute_paired_d | Computes Cliff's dependent d-statistics based on cell frequencies.
Cliff_independent | Computes the independent groups d-statistic comparing the two vectors provided.
Cliff_independent_from_matrix | Computes d-statistic from dominance matrix provided.
Cliff_independent_from_table | Computes independent group's d-statistic from the matrix of frequencies provided.
Cliff_independent_weighted | Computes d-statistic based on scores and integer weights(frequencies) for each group.
Cliff_weighted_d_matrix | Computes weighted version of dominance matrix "d"
coal_g | Degree of disease measured at two points in time for mine workers.
constant_of_integration | Computes the constant of integration of a multinomial sample.

## -- D --

depression | Ratings of severity of patient's depression by two therapists.
dogs | Dehydration in dogs data set.
dreams | Severity of disturbing dreams in adolescent boys, measured at two ages..
dumping | Occurrence of side effects after gastro-intestinal surgery.

## -- E --

esophageal_cancer | Ratings of number of hot drinks consumed by cases with cancer of the esophagus, compared with control subjects.
expand | Converts weighted (x, w) pairs into unweighted data by replicating x[i] w[i] times
expit | Computes the "expit" function - inverse of logit.

## -- F --

family_income | Family income for two years from US census.

## -- G --

gender_vision | Ratings of visual acuity for men and women employed at the Royal Ordinance factories, 1943-1946.
Goodman_constrained_diagonals_parameter_symmetry | Fits the model where some of the delta parameters are constrained to be equal to one another.
Goodman_diagonals_parameter_symmetry | Fit's Goodman's diagonals parameter symmetry model.
Goodman_fixed_parameter | Fits the model with given parameters fixed to specific values.
Goodman_ml | Performs ML estimation of the model.
Goodman_model_i | Fits Goodman's (1979) Model I
Goodman_model_ii | Fits Goodman's (1979) Model II
Goodman_model_ii_star | Fits Goodman's (1979) model II*, where row and column effects are equal.
Goodman_model_i_star | Fits Goodman's (1979) Model I*
Goodman_null_association | Fits Goodman's L. A. (1979) Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories
Goodman_pi | Computes the model-based probability for cell i, j
Goodman_pi_matrix | Computes the full matrix of model-based cell probabilities.
Goodman_symmetric_association_model | Fits the symmetric association model from Goodman (1979). Note the model is a reparameterized version of the quasi-symmetry model, so the quasi-symmetry model has the same fit indices.
Goodman_uniform_association | Fits Goodman's (1979) uniform association model

## -- H --

handle_max_i_i | Case where j == r, i == k == k2
handle_max_i_k | Case where j == r, i != k, i == k2
handle_max_k_k2 | Case where j == r, i != k && i != k2
handle_one_maximum | Case where pi[i, r] with k and k2
handle_tied_below_maximum | Case where i == j, i < r, j < r
handle_tied_maximum | Case where pi[r, r] with k and k2
handle_untied_below_maximum | Case where i != j, i < r && j < r
homicide_black_black | Data about charges of homicide in the state of Florida.
homicide_black_white | Data about charges of homicide in the state of Florida.
homicide_white_black | Data about charges of homicide in the state of Florida.
homicide_white_white | Data about charges of homicide in the state of Florida.
hypothalamus_1 | Measures of men's hypothalamus taken from cadavers. First data set.
hypothalamus_2 | Measures of men's hypothalamus taken from cadavers. Second data set.

## -- I --

interference_12 | Measures of interference in memory recall study.
interference_control_1 | Measures of interference in memory recall study.
interference_control_2 | Measures of interference in memory recall study.
Ireland_marginal_homogeneity | Fits marginal homogeneity model
Ireland_mdis | Computes the MDIS between the two matrices provided.
Ireland_normalize_for_truncation | Renormalize counts to account for truncation of diagonal
Ireland_quasi_symmetry | Fit for quasi-symmetry model. Obtained by subtraction, so no model-based probabilities.
Ireland_quasi_symmetry_model | Fitss the quasi-symmetry model.
Ireland_symmetry | Fits symmetry model.
is_invertible | Tests whether a square matrix is invertible (non singular)
is_missing_or_infinite | Determines if its argument is not a valid number.

## -- K --

kappa | Computes Cohen's 1960 kappa coefficient

## -- L --

likelihood_ratio_chisq | Computes the likelihood ratio G^2 measure of fit.
loadRData | Function to load a data set written out using save().
logit | Computes the log-odds (logit) for the value provided
log_likelihood | Computes the multinomial log(likelihood).
log_linear_add_all_diagonals | Adds indicator variables for the diagonal cells in table n.
log_linear_append_column | Appends a column to an existing design matrix.
log_linear_create_coefficient_names | Creates missing column names
log_linear_create_linear_by_linear | Creates a vector containing the linear-by-linear vector.
log_Linear_create_log_n | Computes the logs of the cell frequencies.
log_linear_equal_weight_agreement_design | Creates design matrix for model with main effects and a single agreement parameter delta.
log_linear_fit | Fits a log-linear model to the data provided, using the design matrix provided. Names for the effects will be "rows1", "cols1" etc. If there are remaining entries, they can be specified as the "effect_names" character vector. This function is a wrapper around a call to glm() that handles some of the details of the call and packages the output in a more convenient form.
log_linear_main_effect_design | Design matrix for baseline independence model with main effects for rows and columns.
log_linear_matrix_to_vector | Converts a matrix of data into a vector suitable for use in analysis with the design matrices created. Unlike simply calling vector() on the matrix the resulting vector is organized by rows, then columns. This order corresponds to the order in the design matrix.
log_linear_quasi_symmetry_model_design | Creates the design matrix for a quasi-symmetry design
log_linear_remove_column | Removes a column from an existing design matrix.
log_linear_symmetry_design | Creates design matrix for symmetry model.

## -- M --

McCullagh_compute_condition | Compute the linear constraint on psi elements for identifiablity.
McCullagh_compute_cumulatives | Computes the model-based cumulative probability matrices pij and qij
McCullagh_compute_cumulative_sums | Computes cumulative sums for rows,
McCullagh_compute_c_plus | Computes sums c+ used in maximizing the log(likelihod)
McCullagh_compute_df | Computes the degrees of freedom for the model
McCullagh_compute_gamma | Computes gamma from x and beta
McCullagh_compute_gamma_from_phi | Computes value of gamma from phi. Inverse of usual computation.
McCullagh_compute_gamma_plus_1_from_phi | Computes value of gamma[j + 1] from phi.
McCullagh_compute_generalized_cumulatives | Coompute the model-based cumulative probabilities pij and qij.
McCullagh_compute_generalized_pi | Cpompute matrix pi under generalized model.
McCullagh_compute_lambda | Computes lambda, log of cumulative odds.
McCullagh_compute_log_l | Computes the log(likelihood) for the general nonlinear model.
McCullagh_compute_Nij | Compute the observed sums Nij
McCullagh_compute_omega | Compute the value of the Lagrange multiplier for the constraint on psi.
McCullagh_compute_phi | Computes phi based on gamma
McCullagh_compute_phi_matrix | Compute matrix of model-based logits
McCullagh_compute_pi | Compute the regular (non-cumulative) model-based pi values
McCullagh_compute_pi_from_beta | Computes matrix of p-values pi based on x and current value of beta.
McCullagh_compute_pi_from_gamma | Compute the cell probabilities pi from gamma.
McCullagh_compute_regression_weights | Computes regression weights w; R_dot_j * (N - R_dot_j[j]) * (n_do_j[j] a= na_dot_j[j+ 1] )
McCullagh_compute_s_plus | Compute sums too use in maximizing log(likelihood)
McCullagh_compute_update | Compute the Newton-Raphson update.
McCullagh_compute_z | Computes Z, where z is w * lambda.
McCullagh_conditional_symmetry | Fits the McCullagh (1978) conditional-symmetry model.
McCullagh_conditional_symmetry_compute_s | Computes sums used in maximizing theta.
McCullagh_conditional_symmetry_initialize_phi | Initializes symmetry matrix phi
McCullagh_conditional_symmetry_maximize_phi | Maximizes log(likelihood) wrt phi.
McCullagh_conditional_symmetry_maximize_theta | Maximizes the log(likelihood) wrt theta.
McCullagh_conditional_symmetry_pi | Computes model-based proportions.
McCullagh_derivative_condition_wrt_psi | Derivative of the condition wrt psi[i, j].
McCullagh_derivative_gamma_plus_1_wrt_phi | Derivative of gamma j + 1 wrt phi.
McCullagh_derivative_gamma_wrt_phi | Derivative of gamma wrt phi.
McCullagh_derivative_gamma_wrt_y | Derivative of y wrt gamma.
McCullagh_derivative_lagrangian_wrt_delta | Derivative of Lagrange multiplier wrt scalar delta.
McCullagh_derivative_lagrangian_wrt_delta_vec | Derivative of Lagrangian wrt delta_vec.
McCullagh_derivative_lagrangian_wrt_psi | Derivative of Lagrangian wrt psi[i1, j1].
McCullagh_derivative_log_l_wrt_alpha | Derivative of log(likelihood) wrt alpha[index].
McCullagh_derivative_log_l_wrt_beta | Derivative of log(likelihood) wrt beta, as given in appendix of McCullagh.
McCullagh_derivative_log_l_wrt_c | Derivative of log(likelihood) wrt c.
McCullagh_derivative_log_l_wrt_delta | Derivative of log(likelihood) wrt delta (scalar or vector0.
McCullagh_derivative_log_l_wrt_delta_vec | Derivative of log(likelihood) wrt delta_vec[k].
McCullagh_derivative_log_l_wrt_params | Derivative of log(likelihood) wrt parameters.
McCullagh_derivative_log_l_wrt_phi | Derivative of log(likelihood) wrt phi[i, j]
McCullagh_derivative_log_l_wrt_psi | Derivative of log(likelihood) wrt psi.
McCullagh_derivative_omega_wrt_alpha | Derivative of Lagrange multiplier omega wrt alpha[index].
McCullagh_derivative_omega_wrt_c | Derivative of Lagrange multiplier omega wrt c.
McCullagh_derivative_omega_wrt_delta | Derivative of Lagrange multiplier omega wrt scalar delta.
McCullagh_derivative_omega_wrt_delta_vec | Derivative of Lagrange multiplier omega wrt vector delta[k].
McCullagh_derivative_omega_wrt_psi | Derivative of Lagrange multiplier omega wrt psi[i, j].
McCullagh_derivative_phi_wrt_gamma | Derivative of phi wrt gamma.
McCullagh_derivative_pij_wrt_alpha | Derivative of pij[i, j] wrt alpha[index]
McCullagh_derivative_pij_wrt_c | Derivative pij[i, j] wrt c.
McCullagh_derivative_pij_wrt_delta | Derivative of pij[i, j] wrt scalar delta.
McCullagh_derivative_pij_wrt_delta_vec | Derivative pij[i,j] wrt vector delta[k].
McCullagh_derivative_pij_wrt_psi | Derivative of pij[a, b] wrt psi[h, k]
McCullagh_derivative_pi_wrt_alpha | Derivative of pi[i, j] wrt alpha[index].
McCullagh_derivative_pi_wrt_c | Derivative pi[i, j] wrt c.
McCullagh_derivative_pi_wrt_delta | Derivative of pi[i, j] wrt delta.
McCullagh_derivative_pi_wrt_delta_vec | Derivative pi[i, j] wrt delta[k].
McCullagh_derivative_pi_wrt_psi | Derivative of pi[i, j] wrt psi[i1, j1].
McCullagh_extract_weights | Extracts the weights to convert cumulative model-based probabilities to regular probabilities.
McCullagh_fit_location_regression_model | Fit location model
McCullagh_generalized_palindromic_symmetry | Generalized version of palindromic symmetry model
McCullagh_generalized_pij_qij | Computes culuative model probabilities for the generalized model using vector delta.
McCullagh_generate_names | Generates names to label the parameters.
McCullagh_get_statistics | Computes summary statistics needed to compute estimate of delta.
McCullagh_gradient_log_l | Gradient vector of log(likelihood)
McCullagh_hessian_log_l | Hessian matrix of log(likelihood)
McCullagh_initialize_beta | Initializes the beta vector.
McCullagh_initialize_delta | Compute initial values for scalar delta
McCullagh_initialize_delta_vec | Initialize vector delta
McCullagh_initialize_psi | Initialize the symmetry matrix psi
McCullagh_initialize_x | Initialize design matrix for location model.
McCullagh_is_in_constraint_set | Logical test of whether a specific psi will be in the constraint set.
McCullagh_is_pi_invalid | Test whether pi matrix is valid, i.e., 0 < all values.
McCullagh_logistic_model | MCCullagh's logistic model.
McCullagh_logits | Computed cumulative logits.
McCullagh_log_L | Computes the log(likelihood).
McCullagh_maximize_q_symmetry | Maximize the log(likelihood) wrt parameters phi and alpha
McCullagh_newton_raphson_update | Newton-Raphson update.
McCullagh_palindromic_symmetry | McCullagh's palindromic symmetry model
McCullagh_penalized | Computes the penalized value of a derivative by adding the derivative of the penalty to it.
McCullagh_pij_qij | Compute model-based cumulative probabilities
McCullagh_proportional_hazards | Computes the proportional hazards.
McCullagh_quasi_symmetry | Fits McCullagh's (1978) quasi-symmetry model.
McCullagh_q_symmetry_initialize_alpha | Initializes the asymmetry vector alpha
McCullagh_q_symmetry_initialize_phi | Initializes the phi matrix
McCullagh_q_symmetry_pi | Computes the model-based p-values
McCullagh_second_order_lagrangian_wrt_psi_2 | Second derivative of Lagrangian wrt psi^2.
McCullagh_second_order_lagrangian_wrt_psi_alpha | Second derivative of Lagrangian wrt psi[i1, j1] and alpha[index].
McCullagh_second_order_lagrangian_wrt_psi_delta | Second derivative of Lagrangian wrt psi[i1, j1] and delta.
McCullagh_second_order_lagrangian_wrt_psi_delta_vec | Second derivative of Lagrangian wrt psi[i1, j1] and delta_vec[k[.
McCullagh_second_order_log_l_wrt_alpha_2 | Second derivative of log(likelihood) wrt alpha^2.
McCullagh_second_order_log_l_wrt_alpha_c | Second derivative of log(likelihood) wrt alpha[index] and c.
McCullagh_second_order_log_l_wrt_beta_2 | Expected values of second order derivatives of log(likelihood) wrt beta.
McCullagh_second_order_log_l_wrt_c_2 | Second derivative of log(likelihood) wrt c^2.
McCullagh_second_order_log_l_wrt_delta_2 | Second derivative of log(likelihood) wrt delta^2.
McCullagh_second_order_log_l_wrt_delta_alpha | Second derivative of log(likelihood) wrt delta and alpha[index].
McCullagh_second_order_log_l_wrt_delta_c | Second derivative of log(likelihood) wrt scalar delta and c.
McCullagh_second_order_log_l_wrt_delta_vec_2 | Second derivative of log(likelihood) wrt delta_vec^2.
McCullagh_second_order_log_l_wrt_delta_vec_alpha | Second derivative of log(likelihood) wrt delta[k] and alpha[index].
McCullagh_second_order_log_l_wrt_delta_vec_c | Second derivative of log(likeloihood) wrt delta_vec[k] and c.
McCullagh_second_order_log_l_wrt_parms | Expected second order derivatives of log(likelihood)
McCullagh_second_order_log_l_wrt_psi_2 | Second derivative of log(likelihoood) wrt psi^2.
McCullagh_second_order_log_l_wrt_psi_alpha | Second derivative of log(likelihoood) wrt ps[i1, j1] and alpha[index].
McCullagh_second_order_log_l_wrt_psi_c | Second derivative of log(likelihood) wrt psi[i1, j1] and c.
McCullagh_second_order_log_l_wrt_psi_delta | Second derivative of log(likelihood) wrt psi[i1, j1] and scalar delta..
McCullagh_second_order_log_l_wrt_psi_delta_vec | Second derivative of log(likelihood) wrt psi[i1, j1] and delta_vec[k].
McCullagh_second_order_omega_wrt_alpha_2 | Second derivative of Lagrange multiplier omega wrt alpha^2.
McCullagh_second_order_omega_wrt_alpha_c | Second derivative of Lagrange multiplier omega wrt alpha[index] and c.
McCullagh_second_order_omega_wrt_c_2 | Second derivative of Lagrange multiplier omega wrt c^2.
McCullagh_second_order_omega_wrt_delta_2 | Second derivative of Lagrange multiplier omega wrt scalae delta^2.
McCullagh_second_order_omega_wrt_delta_alpha | Second derivative of Lagrange multiplier omega wrt delta and alpha[index].
McCullagh_second_order_omega_wrt_delta_c | Second derivative of Lagrange multiplier omega wrt scalar delta and c.
McCullagh_second_order_omega_wrt_delta_vec_2 | Second derivative of Lagrange multiplier omega wrt delta_vec^2.
McCullagh_second_order_omega_wrt_delta_vec_alpha | Second derivative of Lagrange multiplier omega wrt delta_vec[k] and alpha[index].
McCullagh_second_order_omega_wrt_delta_vec_c | Second derivative of Lagrange multiplier omega wrt delta_vec[k] and c.
McCullagh_second_order_omega_wrt_psi_2 | Second derivative of Lagrange multiplier omega wrt psi^2.
McCullagh_second_order_omega_wrt_psi_alpha | Second derivative of Lagrange multiplier omega wrt psi[i1, j1] and alpha[index].
McCullagh_second_order_omega_wrt_psi_c | Second derivative of Lagrange multiplier omega wrt psi[i1, j1] and c.
McCullagh_second_order_omega_wrt_psi_delta | Second derivative of Lagrange multiplier omega wrt psi and scalar delta.
McCullagh_second_order_omega_wrt_psi_delta_vec | Second derivative of Lagrange multiplier omega wrt psi[i1, j1] and delta_vec[k].
McCullagh_second_order_pi_wrt_alpha_2 | Second derivative of pi[i, j] wrt alpha^2.
McCullagh_second_order_pi_wrt_alpha_c | Second derivaitve of pi[i, j] wrt alpha[index] and c.
McCullagh_second_order_pi_wrt_c_2 | Second order derivative of pi[i, j] wrt c^2.
McCullagh_second_order_pi_wrt_delta_2 | Second order derivative of pi[i, j] wrt scalar delta.
McCullagh_second_order_pi_wrt_delta_alpha | Second order deriviative of pi[i, j] wrt scalar delta and alpha[index]
McCullagh_second_order_pi_wrt_delta_c | Second order derivative of pi[i, j] wrt scalae delta and c.
McCullagh_second_order_pi_wrt_delta_vec_2 | Derivative of pi[i, j] wrt delta^2.
McCullagh_second_order_pi_wrt_delta_vec_alpha | Second order dertivative of pi[i, j] wrtt delta[k] alpha[index].
McCullagh_second_order_pi_wrt_delta_vec_c | Second derivative of pi[i, j] wrt delta[k] and c.
McCullagh_second_order_pi_wrt_psi_2 | Second order derivative wrt psi^2.
McCullagh_second_order_pi_wrt_psi_alpha | Second order derivative of pi[i, j] wrt psi[i1, j1] and alpha[index].
McCullagh_second_order_pi_wrt_psi_c | Second order derivative of pi[i, j] wrt psi[i1, j1] and c.
McCullagh_second_order_pi_wrt_psi_delta | Second order derivaitve of pi wrt pshi and scalar delta.
McCullagh_second_order_pi_wrt_psi_delta_vec | Second order derivaitve of pi[i, j] wrt psi[i1, j1] and kelta[k].
McCullagh_update_parameters | Update the parameters based on Newton-Raphson step.
McCullagh_v_inverse | Compute v_inverse (from appendix).
mental_health | Relationship between child's mental health and parents' socioeconomic status.
model_ii_effects | Gets the effects phi, ksi_i_dot and ksi_dot_j for Model II results.
model_ii_fHat | Computes expected counts for Model II
model_ii_ksi | Gets the effects phi, ksi_i_dot and ksi_dot_j for Model II matrix of odds-ratios.
model_ii_starting_values | Computes crude starting values for Model II
model_ii_star_effects | Gets the effects for Model II*
model_ii_star_fHat | Computes expected counts for Model II*
model_ii_star_update_phi | Updates estimate of phi vector
model_ii_update_alpha | Updates the estimate of the alpha vector for Model II
model_ii_update_beta | Updates the estimate of the beta vector for Model II
model_ii_update_rho | Updates the estimate of the rho vector for Model II
model_ii_update_sigma | Updates the estimate of the sigma vector for Model II
model_i_column_theta | Computes the column association values theta-hat
model_i_effects | Gets the overall effects for Model I.
model_i_fHat | Computes model-based expected cell counts for Model I
model_i_normalize_fHat | Normalizes pi(fHat) to sum to 1.0. If exclude_diagonal is TRUE, the sum of the off-diagonal terms sums to 1.0.
model_i_row_column_odds_ratios | Computes the table of adjacent odds-ratios theta-hat.
model_i_row_theta | Computes the row association values theta-hat
model_i_starting_values | Computes crude starting values for Model I.
model_i_star_effects | Gets the Model I* effects.
model_i_star_fHat | Computes expected frequencies for Model I*
model_i_star_update_theta | Updates the row/column parameters for Model I*.
model_i_update_alpha | Updates the estimate of the alpha vector for Model I
model_i_update_beta | Updates the estimate of the beta vector for Model I
model_i_update_delta | Updates the estimate of the delta vector for Model I
model_i_update_gamma | Updates the estimate of the gamma vector for Model I
model_i_zeta | Computes the overall association theta and the row and column effects zeta
movies | Movie ratings by two film critics, Siskel and Ebert.

## -- N --

new_orleans_data | Agreement between two clinicians on presence of multiple sclerosis based on file.
null_association_fHat | Computes expected counts for null association model

## -- O --

occupational_status | Cross tabulation of father's employment status with son's employment status.

## -- P --

paranoia | Interrater agreement of two psychologists' ratings of paranoia.
pearson_chisq | Computes the Pearson X^2 statistic.

## -- R --

radiology | Interrater agreement of two radiologists diagnosis of severity of carcinoma.

## -- S --

Schuster_compute_df | Computes the degrees of freedom for the model.
Schuster_compute_pi | Compute matrix of model-based proportions pi.
Schuster_compute_starting_values | Computes starting values for the model.
Schuster_derivative_log_l_wrt_kappa | Derivative of log(likelihood) wrt kappa.
Schuster_derivative_log_l_wrt_marginal_pi | Derivative of log(likelihood) wrt marginal_pi[k]
Schuster_derivative_log_l_wrt_v | Derivative of log(likelihood) wrt v[i1, j1]
Schuster_derivative_pi_wrt_kappa | Derivative of pi[i, j] wrt kappa coefficient.
Schuster_derivative_pi_wrt_marginal_pi | Derivative of pi[i, j] wrt marginal_pi[k].
Schuster_derivative_pi_wrt_v | Computes derivative of pi[i, j] wrt v[i1, j1]
Schuster_derivative_v_wrt_v | Computes derivative of v[i1, j1] wrt v[i2, j2]
Schuster_enforce_constraints_on_v | Compute v matrix subject to constraints on rows 1..r-1.
Schuster_gradient | Gradient vector log(L) wrt parameters.
Schuster_hessian | Computes the hessian matrix of second-order partial derivatives of log(L).
Schuster_is_pi_valid | Determines whether the candidate pi matrix is valid.
Schuster_newton_raphson | Performs Newton-Raphson step.
Schuster_second_deriv_log_l_wrt_kappa_2 | Second order partial log(L) wrt kappa^2.
Schuster_second_deriv_log_l_wrt_kappa_v | Second order partial log(L) wrt kappa and v.
Schuster_second_deriv_log_l_wrt_marginal_pi_2 | Second order partial log(L) wrt marginal_pi^2.
Schuster_second_deriv_log_l_wrt_marginal_pi_kappa | Second order partial log(L) wrt marginal_pi and kappa.
Schuster_second_deriv_log_l_wrt_marginal_pi_v | Second order partial log(L) wrt marginal_pi and v.
Schuster_second_deriv_log_l_wrt_v_2 | Second order partial log(L) wrt v^2.
Schuster_second_deriv_pi_wrt_kappa_2 | Second order partial wrt kappa, kappa
Schuster_second_deriv_pi_wrt_kappa_v | Second order partial wrt kappa, v
Schuster_second_deriv_pi_wrt_marginal_pi_2 | Second derivative of pi[i, j] wrt marginal_pi[k]^2
Schuster_second_deriv_pi_wrt_marginal_pi_kappa | Second order partial wrt kappa, marginal_pi
Schuster_second_deriv_pi_wrt_marginal_pi_v | Second order partial pi wrt marginal_pi and v
Schuster_second_deriv_pi_wrt_v_2 | Second order partial wrt v^2
Schuster_solve_for_v | Solves for the last row and diagonal of symmetry matrix v (v-tilde) using constraint equations
Schuster_solve_for_v1 | Solves for the last row and diagonal of symmetry matrix v (parameteer v-tilde) using linear algebra formulation from paper.
Schuster_symmetric_rater_agreement_model | Computes the model that has kappa as a coefficient and symmetry.
Schuster_update | Computes the Newton-Raphson update
Schuster_v_tilde | Computes the common diagonal term v-tilde.
social_status | Social mobility data with father's occupational social status and son's occupational social status.
social_status2 | Social mobility data with father's occupational social status and son's occupational social status. * categories instead of 7 in social status..
Stuart_marginal_homogeneity | Computes Stuart's Q test of marginal homogeneity.

## -- T --

taste | Taste ratings
teachers | Teachers ratings of their students intelligence.
teaching_style | Style of teachers rated by supervisors
tonsils | Relationship between size of child's tonsils and their status as a carrier of a disease.
tv | Interrater agreement of two journalists' evaluation of proposed TV programs.

## -- U --

uniform_association_fHat | Computes expected counts for uniform association model
uniform_association_update_theta | Updates estimate of theta value of the uniform association model

## -- V --

var_kappa | Computes the sampling variance of kappa.
var_weighted_kappa | Computes the sampling variance of weighted kappa.
vision_data | Visual acuity of women factory workers.
vision_data_men | Visual acuity of men factory workers.
von_Eye_diagonal | Fits the diagonal effects model, where each category has its own parameter delta[k].
von_Eye_diagonal_linear_by_linear | Fits the diagonal effects model, where each category has its own parameter delta[k], while also incorporating a linear-by-linear term.
von_Eye_equal_weighted_diagonal | Fits the equal weighted diagonal model, where the diagonals all have an additional parameter delta, with the constraint that delta is equal across all categories.
von_Eye_equal_weight_diagonal_linear | Fits the diagonal effects model, where there is a single delta parameter for all categories, while also incorporating a linear-by-linear term.
von_Eye_linear_by_linear | Fits the basic independent rows and columns model incorporating a linear-by-linear term.
von_Eye_main_effect | Fits the base model with only independent row and column effects.
von_Eye_weight_by_response_category_design | Creates design matrix for weight be response category model.

## -- W --

weighted_cov | Computes the weighted covariance
weighted_kappa | Computes Cohen's 1968 weighted kappa coefficient
weighted_var | Computes the weighted variance
winnipeg_data | Agreement between two clinicians on presence of multiple sclerosis based on file.