McCullagh_newton_raphson_update

Using gradient and hessian, it finds the update direction. Then it tries increassingly
smaller step sizes until the step*update yields a valid pi matrix.

Fit a variety of models to two-way tables with ordered categories.
Most of the models are appropriate to apply to tables of that have correlated ordered
response categories. There is a particular interest in rater data and models for rescore
tables. Some utility functions (e.g., Cohen's kappa and weighted kappa) support
more general work on rater agreement.
Because the names of the models are very similar, the functions that implement them are
organized by last name of the primary author of the article or book that suggested the model,
with the name of the function beginning with that author's name and an underscore. This
may make some models more difficult to locate if one doesn't have the original sources. The
vignettes and tests can help to locate models of interest. For more dertaiils see the following references:
Agresti, A. (1983) <doi:10.1016/0167-7152(83)90051-2> "A Simple Diagonals-Parameter Symmetry And Quasi-Symmetry Model",
Agrestim A. (1983) <doi:10.2307/2531022> "Testing Marginal Homogeneity for Ordinal Categorical Variables",
Agresti, A. (1988) <doi:10.2307/2531866> "A Model For Agreement Between Ratings On An Ordinal Scale",
Agresti, A. (1989) <doi:10.1016/0167-7152(89)90104-1> "An Agreement Model With Kappa As Parameter",
Agresti, A. (2010 ISBN:978-0470082898) "Analysis Of Ordinal Categorical Data",
Bhapkar, V. P. (1966) <doi:10.1080/01621459.1966.10502021> "A Note On The Equivalence Of Two Test Criteria For Hypotheses In Categorical Data",
Bhapkar, V. P. (1979) <doi:10.2307/2530344> "On Tests Of Marginal Symmetry And Quasi-Symmetry In Two And Three-Dimensional Contingency Tables",
Bowker, A. H. (1948) <doi:10.2307/2280710> "A Test For Symmetry In Contingency Tables",
Clayton, D. G. (1974) <doi:10.2307/2335638> "Some Odds Ratio Statistics For The Analysis Of Ordered Categorical Data",
Cliff, N. (1993) <doi:10.1037/0033-2909.114.3.494> "Dominance Statistics: Ordinal Analyses To Answer Ordinal Questions",
Cliff, N. (1996 ISBN:978-0805813333) "Ordinal Methods For Behavioral Data Analysis",
Goodman, L. A. (1979) <doi:10.1080/01621459.1979.10481650> "Simple Models For The Analysis Of Association In Cross-Classifications Having Ordered Categories",
Goodman, L. A. (1979) <doi:10.2307/2335159> "Multiplicative Models For Square Contingency Tables With Ordered Categories",
Ireland, C. T., Ku, H. H., & Kullback, S. (1969) <doi:10.2307/2286071> "Symmetry And Marginal Homogeneity Of An r × r Contingency Table",
Ishi-kuntz, M. (1994 ISBN:978-0803943766) "Ordinal Log-linear Models",
McCullah, P. (1977) <doi:10.2307/2345320> "A Logistic Model For Paired Comparisons With Ordered Categorical Data",
McCullagh, P. (1978) <doi:10.2307/2335224> A Class Of Parametric Models For The Analysis Of Square Contingency Tables With Ordered Categories",
McCullagh, P. (1980) <doi:10.1111/j.2517-6161.1980.tb01109.x> "Regression Models For Ordinal Data",
Penn State: Eberly College of Science (undated) <https://online.stat.psu.edu/stat504/lesson/11> "Stat 504: Analysis of Discrete Data, 11. Advanced Topics I",
Schuster, C. (2001) <doi:10.3102/10769986026003331> "Kappa As A Parameter Of A Symmetry Model For Rater Agreement",
Shoukri, M. M. (2004 ISBN:978-1584883210). "Measures Of Interobserver Agreement",
Stuart, A. (1953) <doi:10.2307/2333101> "The Estimation Of And Comparison Of Strengths Of Association In Contingency Tables",
Stuart, A. (1955) <doi:10.2307/2333387> "A Test For Homogeneity Of The Marginal Distributions In A Two-Way Classification",
von Eye, A., & Mun, E. Y. (2005 ISBN:978-0805849677) "Analyzing Rater Agreement: Manifest Variable Methods".

John R. Donoghue

ordinalTables

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

McCullagh_newton_raphson_update function

<dl><dt>n</dt>
<dd>matrix of observed counts</dd>
<dt>gradient</dt>
<dd>gradient vector</dd>
<dt>hessian</dt>
<dd>hessian matrix</dd>
<dt>psi</dt>
<dd>matrix of symmetry parameters</dd>
<dt>delta</dt>
<dd>scalar or vector of asymmetry parameters</dd>
<dt>alpha</dt>
<dd>vector of asymmetry parameters</dd>
<dt>c</dt>
<dd>scaling factor to ensure pi sums to 1.0. Default is 1.0</dd>
<dt>max_iter</dt>
<dd>maximum number of iterations. Default is 50.</dd>
<dt>verbose</dt>
<dd>should cycle-by-cycle into be printed out. Default is FALSE,
do not print.</dd></dl>

Arguments

Newton-Raphson update. — McCullagh_newton_raphson_update

<dl>

<dt>n</dt>
<dd>matrix of observed counts</dd>


<dt>gradient</dt>
<dd>gradient vector</dd>


<dt>hessian</dt>
<dd>hessian matrix</dd>


<dt>psi</dt>
<dd>matrix of symmetry parameters</dd>


<dt>delta</dt>
<dd>scalar or vector of asymmetry parameters</dd>


<dt>alpha</dt>
<dd>vector of asymmetry parameters</dd>


<dt>c</dt>
<dd>scaling factor to ensure pi sums to 1.0. Default is 1.0</dd>


<dt>max_iter</dt>
<dd>maximum number of iterations. Default is 50.</dd>


<dt>verbose</dt>
<dd>should cycle-by-cycle into be printed out. Default is FALSE,
do not print.</dd>

</dl>

McCullagh_newton_raphson_update: Newton-Raphson update.

Description

Usage

Value

Arguments