Package 'MMDai'

Generate random dataset

Description

This function is used to generate random datasets following mixture of product multinomial distribution

Usage

GenerateData(
  n,
  p,
  d,
  k = 3,
  theta = rdirichlet(1, rep(10, k)),
  psi = InitialPsi(p, d, k)
)

Arguments

n	- number of samples
p	- number of variables
d	- a vector which denotes the number of categories for each variable. It could be distinct among variables.
k	- number of latent classes
theta	- probability for latent class
psi	- probability for specific category

Value

data - generated random dataset, a matrix with n rows and p columns.

Examples

# dimension parameters
n<-200; p<-5; d<-rep(2,p);
# generate complete data
Complete<-GenerateData(n, p, d, k = 3)

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Imputation

Description

This function is used to perform multiple imputation for missing data given the joint distribution.

Usage

Imputation(data, theta, psi)

Arguments

data	- incomplete dataset
theta	- vector of probability for each component
psi	- specific probability for each variable in each component

Value

ImputedData - dataset has been imputated.

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initial psi

Description

This function creates a psi list in that each component has equal weight

Usage

InitialPsi(p, d, k)

Arguments

p	- number of variables
d	- a vector which denotes the number of categories for each variable. It could be distinct among variables.
k	- number of components

Value

psi - a list in that each component has equal weight

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Identify the suitable number of components k

Description

This function is used to find the suitable number of components k.

Usage

kIdentifier(data, d, TT = 1000, alpha = 0.25)

Arguments

data	- data in matrix formation with n rows and p columns
d	- number of categories for each variable
TT	- number of iterations in Gibbs sampler, default value is 1000. T should be an even number for 'burn-in'.
alpha	- hyperparameter that could be regarded as the pseudo-count of the number of samples in the new component

Value

k_est - posterior estimation of k

k_track - track of k in the iteration process

Examples

# dimension parameters
n<-200; p<-5; d<-rep(2,p);
# generate complete data
Complete<-GenerateData(n, p, d, k = 3)
# mask percentage of data at MCAR
Incomplete<-Complete
Incomplete[sample(1:n*p,0.2*n*p,replace = FALSE)]<-NA
# k identify
K<-kIdentifier(data = Incomplete, d, TT = 10)

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Real application dataset

Description

This is a real application dataset. The source of original data is the ratings dataset in (Harper and Konstan (2016) <DOI:10.1145/2827872>). This dataset is used to evaluate the performance of package in real applications.

Author(s)

Chaojie Wang

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Estimate theta and psi in multinomial mixture model

Description

This function is used to estimate theta and psi in multinomial mixture model given the number of components k.

Usage

ParEst(data, d, k, TT = 1000)

Arguments

data	- data in matrix formation with n rows and p columns
d	- number of categories for each variable
k	- number of components
TT	- number of iterations in Gibbs sampler, default value is 1000. T should be an even number for 'burn-in'.

Value

theta - vector of probability for each component

psi - specific probability for each variable in each component

Examples

# dimension parameters
n<-200; p<-5; d<-rep(2,p);
# generate complete data
Complete<-GenerateData(n, p, d, k = 3)
# mask percentage of data at MCAR
Incomplete<-Complete
Incomplete[sample(1:n*p,0.2*n*p,replace = FALSE)]<-NA
# k identify
K<-kIdentifier(data = Incomplete, d, TT = 10)
Par<-ParEst(data = Incomplete, d, k = K$k_est, TT = 10)

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Estimate theta and psi in multinomial mixture model

Description

This function is generate random sample from Dirichlet distribution

Usage

rdirichlet(n = 1, alpha = c(1, 1))

Arguments

n	- sample size
alpha	- parameters in Dirichlet distribution

Value

out - generated data

Examples

# dimension parameters
rdirichlet(n=10,alpha=c(1,1,1))

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