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Fixed a bug with fitting the two-parameter beta-distribution model in the HB.CA(), HB.CA.MC(), and HB.ROC() functions.
Significantly improved computation time for consistency in the HB.CA() and HB.CA.MC() functions.
To reduce the verbosity of the output, the LL.and HB. functions no longer include the positive and negative likelihood ratios as part of their output.
The AMS() and BMS() functions have had some arguments removed. Now only allows for specifying mean, variance (or standard deviation), and location parameters.
The LABMSU() and UABMSL() functions have had arguments removed (skewness and kurtosis) due to arguments being removed from AMS() and BMS().
The Beta.tp.fit() function is significantly simplified and some arguments (alpha andbeta) are removed.
The d/p/q/rBetaMS() functions now includes arguments for specifying lower- and upper-bound location parameters. This allows the mean to be specified outside the [0, 1] interval.
Changes to model fit argument in the LL. and HB. functions.
The classification functions LL.CA(), LL.CA.MC(), HB.CA, and HB.CA.MC() functions now allows for specifying not to perform model-fit testing by passing NULL to the modelfit argument.
Fixed a bug that affected the binning of of observed values. Due to some strange behavior in R that resulted from scaling and re-scaling values, observations would sometimes be assigned to the wrong bins. This should now be fixed.
Added arguments to the mdlfit.gfx() function that allows for manually controlling a number of plot aesthetics.
Added an implementation of the Hanson-Brennan approach to classification accuracy and consistency.
The HB.CA() and HB.MC.CA() functions for binary and multiple classifications, respectively.
The HB.ROC() function for ROC analysis.
Added d/p/r functions for Lord’s two-term approximation to the compound binomial distribution (xcBinom()).
Added d/p/r functions for Beta compound-Binomial distributions where the compound Binomial is Lord’s two-term approximation (xBetacBinom()).
Added the mdlfit.gfx() as a visual aid to gauge the severity of model misfit for the LL and HB approaches.
Added d/p/r functions for Beta-Binomial distributions (d/p/rBetaBinom(), no q function as of yet).
Added the betabinomialmoments() function for calculating raw-, central-, and standardized moments of Beta-Binomial distributions.
Added the R.ETL() function for calculating the model-implied reliability of test-scores given the “Effective Test Length” of Livingston and Lewis (1995), and the mean, variance, and minimum and maximum possible scores of the observed-score distribution.
Added the mdo() function which allows for estimating McDonald’s Omega reliability coefficient. Requires that there are no negative item-covariances.
Added the MC.out.tabular() function which can be used to organize the accuracy and consistency output from the LL.CA.MC() function in tabular format. The MC.out.tabular() function takes the output of the LL.CA.MC() function as input.
Changes to the model-fit test procedure for the LL.CA()and LL.CA.MC() functions. The initial number of bins are now set to 100 and the minimum bin-size is set to 10. The bins are now only grouped into the expected number of observations rather than both expected and observed. The behaviour of this model-fit test-procedure is still under scrutiny and should as of yet be considered an experimental approximation procedure.
Added betamode() and betamedian() functions that allow for calculating the mode and median (respectively) of two- and four-parameter Beta distributions.
Added modelfit arguments to the LL.CA() and LL.CA.MC() functions that allow for controlling the maximum number of- and minimum size of the bins that are to be used for the chi-square test of model fit. Tuning the maximum number and minimum size of the bins should facilitate model-fit testing if the default settings does not result in sufficient degrees of freedom to perform the significance-test.
Fixed bug in the LL.CA.MC() function regarding the assembly of the consistency matrix when more than two categories were included which resulted in some entries having slightly too large values. This change results in slight changes to the estimated consistency-indices (now more precise).
The LL.CA() and LL.CA.MC() functions no longer issue warnings if parameter estimates are out of bounds if the true.model argument is specified to "2P" and the failsafe argument is set to TRUE (the default).
Major updates to the classification accuracy and consistency functionalities:
Added new LL.ROC() functionality, providing the option to give the ROC-curve a classic, “staircase” look. This option is made the default.
Added the LL.CA.MC() function extending the Livingston and Lewis approach to using multiple cut-points. The output of this function can grow quite verbose when operating with several cut-points, as diagnostic performance and consistency indices are estimated and reported for each group separately.
Removed the error.model argument of the LL.CA() function. In essence, this means that one can no longer specify a beta error model.
Added model-fit functionality to the LL.CA() function. The model-fit is examined by comparing observed and model-expected frequencies by binning frequencies into bins of at least 10 expected and observed frequencies. According to Lord, this model fit procedure has N-bins - 4 degrees of freedom, meaning that model-fit cannot be examined if a grouping of the observed-score distribution reduces to fewer than 5 bins.
Added the gchoose() function generalizing the base-R choose() function to work with non-integers and positive integers by calculating the factorials of the Binomial coefficient by drawing on the Gamma distribution.
Added new set of d/p/q/r functions for a new distribution: The “Gamma-Binomial” distribution. This distribution extends the Binomial distribution to all positive real numbers. Not defined for negative integers.
dGammaBinom(): Probability Density Distribution for the Gamma-Binomial distribution.
pGammaBinom(): Cumulative Probability Density Distribution for the Gamma-Binomial distribution.
qGammaBinom(): Quantile function for the Gamma-Binomial distribution. Calls the pGammaBinom() function and utilizes a bisecting search-algorithm to find the number of “successful trials” corresponding to the quantile in question. This algorithm is rather slow so the function might take longer to find the appropriate quantile than what one might be used to.
rGammaBinom(): Random number generation for the Gamma-Binomial distribution. Calls the qGammaBinom() function. Since the qGammaBinom() function searches for the appropriate values using a rather inefficient search-algorithm (bisection), this random-number generation is somewhat slow.
Added the binomialmoments() function, which allows for calculating the raw, central, and standardized moments of Binomial distributions (for which the Beta distribution is the conjugate prior).
Changes to the LL.ROC() function.
Changed the internal behavior of the function to estimate the true-score distribution only once. This should greatly improve the time required to produce the plots.
Added the locate argument where it is possible to ask the function to locate the operational cut-point at which the values of sensitivity or NPV are greater than or equal to some value, or specificity or PPV are lesser than or equal to some value.
Added the maxAcc argument to locate the cut-point at which the Accuracy statistic is maximized.
The raw-output print-out now contains the cut-point specific Accuracy, PPV, and NPV statistics as well.
Changes to the afac and dfac functions.
"product" as part of the method argument.Changes to the tsm function.
tsm function now calls the dfac function with the direct-arithmetic method for calculating descending factorials as default. In order to use the gamma function rather than direct arithmetic, specify any value other than “product” as part of the method argument.Correction to the LL.CA() function. The Binomial error distribution evaluated up to and including the cut-point. The intended behaviour was to evaluate up to but NOT including the cut-point. Prior to this correction, it is expected that the LL.CA() function will have underestimated accuracy somewhat.
dBeta.pBinom() function as well, which is contrary to the default behavior of base-R’s pbinom() function.Fixed a bug with the true-score distribution fitting procedure in the Beta.tp.fit() that could occur for low integer values.
Minor changes to the documentation for various functions.
Added possibility of calculating descending (falling) and ascending (rising) factorials by means of the dfac() and afac()functions.
Added tsm() argument for calculating raw moments of the true-score distribution under the Livingston and Lewis approach.
Added confmat() function for organizing supplied values of true and false positives and negatives into a confusion matrix.
Changes to the LL.ROC() function. Now allows for specifying the lower- and upper-bound parameters of the true-score distribution should “2P” be specified.
A Shiny application providing a GUI for the Livingston and Lewis approach functionality of the package has been developed and can be found at https://hthaa.shinyapps.io/shinybeta/
The “3P” functionality of Beta.tp.fit(), LL.CA() and LL.ROC has been removed, as it did not perform satisfactorily.
The true.model argument of the Beta.tp.fit() function now includes a "3P" option, allowing for the specification of one location-parameter (l or u) and estimating the remaining location-parameter and the shape-parameters (alpha and beta) so as to make the resulting distribution have the same skewness and kurtosis as the estimated true-score distribution.
The AMS() and BMS() functions now issue warnings if there was not enough information supplied to calculate the target parameter.
The ETL() function: For the sake of argument consistency, the l and u arguments are not renamed min and max, respectively.
Added a number of new functions for working with Beta distributions.
The new LABMSU() function allows for finding the lower-bound parameter for the four-parameter Beta distribution by supplying the shape-parameters and moments of the resulting distribution, and (optionally) the upper-bound location parameter.
The new UABMSU() function allows for finding the upper-bound parameter for the four-parameter Beta distribution by supplying the shape-parameters and moments of the resulting distribution, and (optionally) the lower-bound location parameter.
Added additional functionality to some existing functions, allowing for specifying the lower- and upper-bounds, and/or moments of the resulting distribution.
The AMS() function now includes l and u arguments, finding the Alpha shape parameter necessary to produce a Beta distribution with target moments and specified lower and upper bounds of the resulting distribution.
The BMS() function now includes l and u arguments, finding the Beta shape parameter necessary to produce a Beta distribution with target moments and specified lower and upper bounds of the resulting distribution.
The Beta.2p.fit() function, essentially a wrapper-function for AMS() and BMS(), now includes l and u arguments for specifying the bounds for the resulting distribution.
Functions relating to estimating classification accuracy and consistency:
Beta.tp.fit(), LL.CA(), and LL.ROC():
Added true.model argument allowing for greater control over the true-score estimation procedure in.
The true.model allows for specifying whether to fit four- or two-parameter Beta distribution to the estimated moments of the true-score distribution.
Currently, the options for the argument are “4P” and “2P”. Further options might be added in the future.
The Beta.tp.fit() function:
Now allows for specifying the lower- and/or upper bounds of the two-parameter solutions.
Now allows for specifying that the fitted distribution should estimate two parameters rather than the default of four. Estimates then the parameters necessary to produce a distribution with the same mean and variance as the estimated true-score distribution, given specified moments, shape- and location parameters (default is l = 0 and u = 1).
Added the option of specifying the true-score distribution moments (sans a functional form) as output rather than the estimated parameters of the Beta true-score distribution in the new output argument. The default is to retrieve the estimated parameters of the Beta true-score distribution.
When parameters is specified in the output argument, the effective test length is included as part of the output. As such, the default output of the Beta.tp.fit() function is now complete for the purposes of being used as input for the LL.CA() function.
The LL.CA() function:
The override and failsafe arguments:
The override argument is rendered inert, to be removed in a later version.
The failsafe argument is introduced to replace the override argument. It is essentially an inversion of the override argument.
The above change is to streamline and make consistent arguments structures across functions.
General code cleaning:
Changed some argument names so as to have the names be consistent across functions. Argument locations in the function calls remain unchanged.
Function arguments previously named lt now named lower.tail.
Function arguments previously named a or b now named alpha and beta (respectively).
Function arguments previously named var now named variance.
Added the possibility of specifying a Beta error model for the LL.ROC() function by way of the true.model argument.
Additional correction of typographical errors in documentation.
Fixed some typographical errors in documentation.
Minor modification to LL.CA() where the function now won’t automatically terminate if true-score distribution fitting procedure produces NA or NaN estimates.
True-score distribution fitting now performed using the new Beta.tp.fit() function.
The grainsize argument is now fully removed from LL.CA().
Added additional checks and diagnostics in LL.CA(), issuing warnings for aberrant events.
If a list of parameter values are supplied in place of a score-vector, it is now necessary to supply an etl (effective test length) parameter as well. See documentation for the ETL() function for more information.
Fixed an error in the fitting procedure of Beta.4P.fit() which occurred during positive skew.
Added the Beta.tp.fit() function for estimating four-parameter Beta distribution parameters for an underlying true-score distribution, assuming that the observations are generated from a Beta-Binomial model.
Fixed the LL.ROC() function which stopped working after the previous update.
grainsize argument.Added functionality for calculating consistency statistics by way of the new ccStats() function.
Substantial developments concerning primarily the LL.CA() function, adding functionality and improving performance.
Added calculation of consistency statistics by calling the new ccStats() function.
Added output argument indicating which statistics to calculate. Default is to compute both accuracy and consistency.
Calculation of distribution-based output now utilizes the integrate() function.
grainsize argument inert, as it was used for the previous method.Added possibility of supplying list of custom parameter values for the four-parameter Beta true-score distribution, forgoing the need to estimate one.
Added override argument providing the possibility of overriding the default fail-safe reverting to a two-parameter Beta true-score distribution, should the fitting procedure produce impermissible parameter estimates.
Fixed small typographical errors in documentation.
Added the cba() function for computing Cronbach’s alpha.
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They may not be fully stable and should be used with caution. We make no claims about them.