Title: Imputation Methods for Multivariate Multinomial Data
Version: 0.8.4
Description: Implements imputation methods using EM and Data Augmentation for multinomial data following the work of Schafer 1997 <ISBN: 978-0-412-04061-0>.
Depends: R (≥ 3.5),
Imports: gtools (≥ 3.3), methods, parallel, Rcpp (≥ 0.11.4), data.table (≥ 1.14.2)
License: GPL-3
LazyData: true
Suggests: testthat, knitr, R.rsp, covr
LinkingTo: Rcpp
RoxygenNote: 7.1.2
Encoding: UTF-8
VignetteBuilder: knitr, R.rsp
Collate: 'RcppExports.R' 'class_imputeMulti.R' 'data-tract2221.R' 'data_dep_prior_multi.R' 'imputeMulti-package.R' 'int-count_levels.R' 'int-impute_multinomial.R' 'int-search_z_Os_y.R' 'int-splitRows.R' 'merge_imputed.R' 'methods_imputeMulti.R' 'multinomial_data_aug.R' 'multinomial_em.R' 'multinomial_impute.R' 'multinomial_stats.R'
NeedsCompilation: yes
Packaged: 2023-02-18 19:30:34 UTC; awhitworth
Author: Alex Whitworth [aut, cre]
Maintainer: Alex Whitworth <whitworth.alex@gmail.com>
Repository: CRAN
Date/Publication: 2023-02-18 20:10:02 UTC

Data Dependent Prior for Multinomial Distribution

Description

Creates a data depedent prior for p-dimensional multinomial distributions using a conjugate prior (eg Dirichlet(\alpha)) based on 20

Usage

data_dep_prior_multi(dat)

Arguments

dat

A data.frame. All variables must be factors

Value

A data.frame containing identifiers for all possible P(Y=y) and the associated prior-counts, \alpha

References

Darnieder, William Francis. Bayesian methods for data-dependent priors. Dissertation. The Ohio State University, 2011.

See Also

expand.grid

Class "imputeMulti"

Description

A multivariate multinomial model imputed by EM or Data Augmentation is represented as a mod_imputeMulti object. A complete dataset and model is represented as an imputeMulti object. Inherits from mod_imputeMulti. Additional slots are supplied for (1) the call to multinomial_impute; (2) the missing and imputed data; and (3) the number of observations with missing values.

Usage

## S4 method for signature 'imputeMulti'
show(object)

get_imputations(object)

## S4 method for signature 'imputeMulti'
get_imputations(object)

n_miss(object)

Arguments

object

an object of class "imputeMulti"

Slots

Gcall

the call to multinomial_impute

method

the modeling method

mle_call

the call to the estimation function

mle_iter

the number of iterations in estimation

mle_log_lik

the final log-likelihood

mle_cp

the conjugate prior if any

mle_x_y

the MLE estimate of the sufficient statistics and parameters

data

a list of the missing and imputed data

nmiss

the number of observations with missing data

Objects from the class

Objects are created by calls to multinomial_impute, multinomial_em, or multinomial_data_aug.

See Also

multinomial_impute, multinomial_em, multinomial_data_aug

Check imputeMulti Class

Description

Function that checks if the target object is a imputeMulti object.

Usage

is.imputeMulti(x)

Arguments

x

any R object.

Value

Returns TRUE if its argument has class "imputeMulti" among its classes and FALSE otherwise.

Check mod_imputeMulti Class

Description

Function that checks if the target object is a mod_imputeMulti object.

Usage

is.mod_imputeMulti(x)

Arguments

x

any R object.

Value

Returns TRUE if its argument has class "mod_imputeMulti" among its classes and FALSE otherwise.

Merge imputed data and original dataset

Description

Merge the imputed dataset from an imputeMulti object with the original dataset. Merging is done by rownames, since imputeMulti maintains row-order during imputation.

Usage

merge_imputed(impute_obj, y, ...)

Arguments

impute_obj

An object of class "imputeMulti".

y

The dataset from which the missing data was imputed.

...

Arguments to be passed to other methods

Class "mod_imputeMulti"

Description

A multivariate multinomial model imputed by EM or Data Augmentation is represented as a mod_imputeMulti object. A complete dataset and model is represented as an imputeMulti object. Slots for mod_imputeMulti objects include: (1) the modeling method; (2) the call to the estimation function; (3) the number of iterations in estimation; (4) the final log-likelihood; (5) the conjugate prior if any; (6) the MLE estimate of the sufficient statistics and parameters.

Usage

## S4 method for signature 'mod_imputeMulti'
show(object)

get_parameters(object)

## S4 method for signature 'mod_imputeMulti'
get_parameters(object)

get_prior(object)

## S4 method for signature 'mod_imputeMulti'
get_prior(object)

get_iterations(object)

## S4 method for signature 'mod_imputeMulti'
get_iterations(object)

get_logLik(object)

## S4 method for signature 'mod_imputeMulti'
get_logLik(object)

get_method(object)

## S4 method for signature 'mod_imputeMulti'
get_method(object)

## S4 method for signature 'imputeMulti'
n_miss(object)

Arguments

object

an object of class "mod_imputeMulti"

Slots

method

the modeling method

mle_call

the call to the estimation function

mle_iter

the number of iterations in estimation

mle_log_lik

the final log-likelihood

mle_cp

the conjugate prior if any

mle_x_y

the MLE estimate of the sufficient statistics and parameters

Objects from the class

Objects are created by calls to multinomial_impute, multinomial_em, or multinomial_data_aug.

See Also

multinomial_impute, multinomial_em, multinomial_data_aug

Data Augmentation algorithm for multinomial data

Description

Implement the Data Augmentation algorithm for multvariate multinomial data given observed counts of complete and missing data (Y_obs and Y_mis). Allows for specification of a Dirichlet conjugate prior.

Usage

multinomial_data_aug(
  x_y,
  z_Os_y,
  enum_comp,
  conj_prior = c("none", "data.dep", "flat.prior", "non.informative"),
  alpha = NULL,
  burnin = 100,
  post_draws = 1000,
  verbose = FALSE
)

Arguments

x_y

A data.frame of observed counts for complete observations.

z_Os_y

A data.frame of observed marginal-counts for incomplete observations.

enum_comp

A data.frame specifying a vector of all possible observed patterns.

conj_prior

A string specifying the conjugate prior. One of c("none", "data.dep", "flat.prior", "non.informative").

alpha

The vector of counts \alpha for a Dir(\alpha) prior. Must be specified if conj_prior is either c("data.dep", "flat.prior"). If flat.prior, specify as a scalar. If data.dep, specify as a vector with key matching enum_comp.

burnin

A scalar specifying the number of iterations to use as a burnin. Defaults to 100.

post_draws

An integer specifying the number of draws from the posterior distribution. Defaults to 1000.

verbose

Logical. If TRUE, provide verbose output on each iteration.

Value

An object of class mod_imputeMulti-class.

See Also

multinomial_em, multinomial_impute

Examples

## Not run: 
 data(tract2221)
 x_y <- multinomial_stats(tract2221[,1:4], output= "x_y")
 z_Os_y <- multinomial_stats(tract2221[,1:4], output= "z_Os_y")
 x_possible <- multinomial_stats(tract2221[,1:4], output= "possible.obs")

 imputeDA_mle <- multinomial_data_aug(x_y, z_Os_y, x_possible, n_obs= nrow(tract2221),
                     conj_prior= "none", verbose= TRUE)

## End(Not run)

EM algorithm for multinomial data

Description

Implement the EM algorithm for multivariate multinomial data given observed counts of complete and missing data (Y_obs and Y_mis). Allows for specification of a Dirichlet conjugate prior.

Usage

multinomial_em(
  x_y,
  z_Os_y,
  enum_comp,
  n_obs,
  conj_prior = c("none", "data.dep", "flat.prior", "non.informative"),
  alpha = NULL,
  tol = 5e-07,
  max_iter = 10000,
  verbose = FALSE
)

Arguments

x_y

A data.frame of observed counts for complete observations.

z_Os_y

A data.frame of observed marginal-counts for incomplete observations.

enum_comp

A data.frame specifying a vector of all possible observed patterns.

n_obs

An integer specifying the number of observations in the original data.

conj_prior

A string specifying the conjugate prior. One of c("none", "data.dep", "flat.prior", "non.informative").

alpha

The vector of counts \alpha for a Dir(\alpha) prior. Must be specified if conj_prior is either c("data.dep", "flat.prior"). If flat.prior, specify as a scalar. If data.dep, specify as a vector with key matching enum_comp.

tol

A scalar specifying the convergence criteria. Defaults to 5e-7

max_iter

An integer specifying the maximum number of allowable iterations. Defaults to 10000.

verbose

Logical. If TRUE, provide verbose output on each iteration.

Value

An object of class mod_imputeMulti-class.

See Also

multinomial_data_aug, multinomial_impute

Examples

## Not run: 
 data(tract2221)
 x_y <- multinomial_stats(tract2221[,1:4], output= "x_y")
 z_Os_y <- multinomial_stats(tract2221[,1:4], output= "z_Os_y")
 x_possible <- multinomial_stats(tract2221[,1:4], output= "possible.obs")

 imputeEM_mle <- multinomial_em(x_y, z_Os_y, x_possible, n_obs= nrow(tract2221),
                     conj_prior= "none", verbose= TRUE)

## End(Not run)

Impute Values for missing multinomial values

Description

Impute values for multivariate multinomial data using either EM or Data Augmentation.

Usage

multinomial_impute(
  dat,
  method = c("EM", "DA"),
  conj_prior = c("none", "data.dep", "flat.prior", "non.informative"),
  alpha = NULL,
  verbose = FALSE,
  ...
)

Arguments

dat

A data.frame. All variables must be factors.

method

c("EM", "DA") A string specifying EM or Data Augmentation (DA)

conj_prior

A string specifying the conjugate prior. One of c("none", "data.dep", "flat.prior", "non.informative").

alpha

The vector of counts \alpha for a Dir(\alpha) prior. Must be specified if conj_prior is either c("data.dep", "flat.prior"). If flat.prior, specify as a scalar. If data.dep, specify as a vector with key matching enum_comp.

verbose

Logical. If TRUE, provide verbose output on each iteration.

...

Arguments to be passed to other methods

Value

An object of class imputeMulti-class

References

Schafer, Joseph L. Analysis of incomplete multivariate data. Chapter 7. CRC press, 1997.

See Also

data_dep_prior_multi, multinomial_em

Examples

## Not run: 
 data(tract2221)
 imputeEM <- multinomial_impute(tract2221[,1:4], method= "EM",
                   conj_prior = "none", verbose= TRUE)
 imputeDA <- multinomial_impute(tract2221[,1:4], method= "DA",
                   conj_prior = "non.informative", verbose= TRUE)

## End(Not run)

Multinomial Sufficient Statistics

Description

Calculate observed-data sufficient statistics, marginally-observed summary statistics or enumerate all possible observed patterns from a multivariate multinomial dataset.

Usage

multinomial_stats(dat, output = c("x_y", "z_Os_y", "possible.obs"))

Arguments

dat

A data.frame. All variables must be factors.

output

A string specifying the desired output. One of c("x_y", "z_Os_y", "possible.obs"). "x_y" indicates the observed-data sufficient statistics, "z_Os_y" indicates the marginally-observed summary statistics, and "possible.obs" indicates the possible observed patterns.

Value

A data.frame containing either sufficient statistics or possible observed patterns.

Examples

## Not run: 
 data(tract2221)
 obs_suff_stats <- multinomial_stats(tract2221, output= "x_y")
 marg_obs_suff_stats <- multinomial_stats(tract2221, output= "z_Os_y")

## End(Not run)

Summarizing imputMulti objects

Description

summary method for class "imputeMulti"

Usage

## S4 method for signature 'imputeMulti'
summary(object, ...)

Arguments

object

an object of class "imputeMulti"

...

further arguments passed to or from other methods.

Summarizing mod_imputMulti objects

Description

summary method for class "mod_imputeMulti"

Usage

## S4 method for signature 'mod_imputeMulti'
summary(object, ...)

Arguments

object

an object of class "mod_imputeMulti"

...

further arguments passed to or from other methods.

Calculate the sup of L1 distance between x and y

Description

sup of L1 distance between x and y

Usage

supDistC(x, y)

Arguments

x

A numeric vector

y

A numeric vector

Value

a numeric scalar.

Observational data on individuals living in census tract 2221

Description

A dataset containing attributes of 3974 individuals living in census tract 2221 in Los Angeles County, CA. Data comes from the 5-year American Community Survey with end year 2014. Missing values have been inserted.

Usage

tract2221

Format

A data.frame with 3974 rows and 10 variables. All variables are of class factor:

age

The individual's age coded in roughly 5 year age buckets.

gender

The indiviudals gender – Male, Female

marital_status

The individuals marital status. Takes one of 5 levels: never_mar never married; married married; mar_apart married but living apart; divorced divorced; and widowed widowed

edu_attain

The individual's educational attainment. Takes one of 7 levels: lt_hs less than high school; some_hs completed some high school but did not graduate; hs_grad high school graduate; some_col completed some college but did not graduate; assoc_dec completed an associates degree; ba_deg obtained a bachelors degree; grad_deg obtained a graduate or professional degree

emp_status

The individuals employment status. Takes one of 3 levels: employed individual is in the labor force and employed; unemployed individual is in the labor force and unemployed; not_in_labor_force individual is not in the labor force

nativity

The individual's nativity status. Takes one of 4 values: born_state_residence born in the state of residence; born_other_state born in another US state; born_out_us a US citizen born outside the US; foreigner foreign born

pov_status

The individual's poverty status in the past year. Takes one of 2 levels: below_pov_level below the poverty level; at_above_pov_level at or above the poverty level

geog_mobility

The individual's geographic mobility in the last year. Takes one of 5 values: same house lived in the same house; same county moved within the same county; same state moved within the same state; same state moved from a different county within the same state; diff state moved from a different state; moved from abroad moved from another country

ind_income

The individual's annual income. Takes one of 9 levels: no_income no income; 1_lt10k income <$10,000; 10k_lt15k $10000-$14999; 15k_lt25k $15000-$24999; 25k_lt35k $25000-$34999; 35k_lt50k $35000-$49999; 50k_lt65k $50000-$64999; 65k_lt75k $65000-$74999; gt75k $75000+

race

The individual's ethnicity.