# multibridge v1.1.0

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## Evaluating Multinomial Order Restrictions with Bridge Sampling

Evaluate hypotheses concerning the distribution of multinomial proportions using bridge sampling. The bridge sampling routine is able to compute Bayes factors for hypotheses that entail inequality constraints, equality constraints, free parameters, and mixtures of all three. These hypotheses are tested against the encompassing hypothesis, that all parameters vary freely or against the null hypothesis that all category proportions are equal. For more information see Sarafoglou et al. (2020) <doi:10.31234/osf.io/bux7p>.

# multibridge: Evaluating Multinomial Order Restrictions with Bridge Sampling

Evaluates hypotheses concerning the distribution of multinomial proportions using bridge sampling. The bridge sampling routine is able to compute Bayes factors for hypotheses that entail inequality constraints, equality constraints, free parameters, and a mix of all three. These hypotheses are tested against the encompassing hypothesis, that all parameters vary freely.

## Installation

System requirement is the library mpfr with a version bigger than 3.0.0. To install mpfr, you need a C compiler, preferably GCC. Detailed information on how to install mpfr are available at https://www.mpfr.org/mpfr-current/mpfr.html.

On Mac you can install mpfr through the Terminal (assuming that brew is installed on your machine).

brew install mpfr


On Debian or Ubuntu you can install mpfr through the Terminal:

sudo apt-get install libmpfr-dev


You can install the released version of multibridge from CRAN with:

install.packages("multibridge")


And the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("ASarafoglou/multibridge")


## Example

This is a basic example which shows you how to solve a common problem:

library("multibridge")
# data
x <- c(3, 4, 10, 11, 7, 30)
# priors
a <- c(1, 1, 1, 1, 1, 1)
# category labels
factor_levels <- c('theta1', 'theta2',
'theta3', 'theta4',
'theta5', 'theta6')
# constrained hypothesis
Hr            <- c('theta1', '<',  'theta2', '&',
'theta3', '=', 'theta4', ',',
'theta5', '<', 'theta6')
output <- mult_bf_informed(x, Hr, a, factor_levels, seed=2020, niter=2e3)

m1 <- summary(output)
m1
#> Bayes factor analysis
#>
#>  Hypothesis H_e:
#>  All parameters are free to vary.
#>
#>  Hypothesis H_r:
#>  theta1 < theta2 & theta3 = theta4 , theta5 < theta6
#>
#> Bayes factor estimate LogBFer:
#>
#> -2.4239
#>
#> Based on 1 independent equality-constrained hypothesis
#>  and 2 independent inequality-constrained hypotheses.
#>
#> Relative Mean-Square Error:
#>
#> 6.29e-05
#>
#> Posterior Median and Credible Intervals Of Marginal Beta Distributions:
#>           alpha   beta   2.5%    50% 97.5%
#> 1 theta1 1 + 3  5 + 62 0.0158 0.0522 0.120
#> 2 theta2 1 + 4  5 + 61 0.0236 0.0664 0.140
#> 3 theta3 1 + 10 5 + 55 0.0811 0.1520 0.247
#> 4 theta4 1 + 11 5 + 54 0.0918 0.1660 0.264
#> 5 theta5 1 + 7  5 + 58 0.0507 0.1090 0.195
#> 6 theta6 1 + 30 5 + 35 0.3240 0.4360 0.553


## Functions in multibridge

 Name Description mult_bf_inequality Computes Bayes Factors For Inequality Constrained Multinomial Parameters journals Prevalence of Statistical Reporting Errors generate_restriction_list Creates Restriction List Based On User Specified Informed Hypothesis mult_bf_informed Evaluates Informed Hypotheses on Multinomial Parameters print.summary.bmult_bridge print method for class summary.bmult_bridge summary.bmult summary method for class bmult restriction_list S3 method for class restriction_list.bmult samples.bmult Extracts prior and posterior samples (if applicable) from an object of class bmult mult_tsampling Samples From Truncated Dirichlet Density tbinom_trans Transforms Truncated Beta Samples To Real Line peas Mendelian Laws of Inheritance bridge_output.bmult Extracts bridge sampling output from object of class bmult lifestresses Memory of Life Stresses mult_bf_equality Computes Bayes Factors For Equality Constrained Multinomial Parameters tdir_backtrans Backtransforms Samples From Real Line To Dirichlet Parameters tbinom_backtrans Backtransforms Samples From Real Line To Beta Parameters print.bmult print method for class bmult plot.summary.bmult Plot estimates summary.bmult_bridge summary method for class bmult_bridge print.bmult_bridge Print method for class bmult_bridge print.summary.bmult print method for class summary.bmult samples S3 method for class 'samples.bmult' restriction_list.bmult Extracts restriction list from an object of class bmult tdir_trans Transforms Truncated Dirichlet Samples To Real Line binom_bf_informed Evaluates Informed Hypotheses on Multiple Binomial Parameters .computeLengthOfRemainingStick Computes Length Of Remaining Stick binom_bf_equality Computes Bayes Factors For Equality Constrained Binomial Parameters .adjustUpperBoundForFreeParameters Adjusts Upper Bound For Free Parameters bridge_output S3 method for class bridge_output.bmult bayes_factor S3 method for class 'bayes_factor.bmult' binom_tsampling Samples From Truncated Beta Densities bayes_factor.bmult Extracts information about computed Bayes factors from object of class bmult binom_bf_inequality Computes Bayes Factors For Inequality Constrained Independent Binomial Parameters No Results!