Process Data Analysis.

ProcData: An R Package for Process Data Analysis

ProcData provides tools for exploratory process data analysis. It contains an example dataset and functions for

• reading responses from a csv file
• process manipulation
• action sequence generators
• feature extraction methods
• fitting and making prediction from sequence models

Installation

Download the package from the download page and execute the following command in R

install.packages(FILENAME, repos = NULL, dependencies = TRUE)

where FILENAME should be replaced by the name of the package file downloaded including its path. The development version can be installed from GitHub with:

devtools::install_github("xytangtang/ProcData")

ProcData depends on packages Rcpp and keras. A C compiler and python are needed. Some functions in ProcData calls functions in keras to fit neural networks. To make sure these functions run properly, execute the following command in R.

library(keras)
install_keras(tensorflow = "1.13.1")

Note that if this step is skipped, ProcData can still be installed and loaded, but calling the functions that depends on keras will give an error.

Contents

Data Structure

ProcData organizes response processes as an object of class proc which is a list containing the action sequences and the timestamp sequences. Functions are provided to summarize and manipulate proc objects.

Dataset

ProcData includes a dataset cc_data of the action sequences and binary item responses of 16920 respondents of item CP025Q01 in PISA 2012. The item interface can be found here. To load the dataset, run

data(cc_data)

cc_data is a list of two elements:

• seqs is a `proc' object.
• responses is a numeric vector containing the binary responses outcomes.

For data stored in csv files, read.seqs can be used to read response processes into R and to organize them into a proc object. In the input csv file, each process can be stored in a single line or multiple lines. The sample files for the two styles are example_single.csv and example_multiple.csv. The processes in the two files can be read by running

seqs1 <- read.seqs(file="example_single.csv", style="single", id_var="ID", action_var="Action", time_var="Time", seq_sep=", ")
seqs2 <- read.seqs(file="example_multiple.csv", style="multiple", id_var="ID", action_var="Action", time_var="Time")

write.seqs can be used to write proc objects in csv files.

Data Generators

ProcData also provides three action sequences generators:

• seq_gen generates action sequences of an imaginary simulation-experiment-based item;
• seq_gen2 generates action sequences according to a given probability transition matrix;
• seq_gen3 generates action sequences from a recurrent neural network. It depends on keras.

Feature Extraction Methods

ProcData implements three feature extraction methods that compress varying length response processes into fixed dimension numeric vectors. The first method extract n-gram features from response processes. The other two methods are based on multidimensional scaling (MDS) and sequence-to-sequence autoencoders (seq2seq AE). Details of the methods can be found here.

N-Gram

Function seq2feature_ngram extracts ngram features from response processes.

seqs <- seq_gen(100)
theta <- seq2feature_ngram(seqs)

MDS

The following functions implement the MDS methods.

• seq2feature_mds extracts K features from a given set of response processes or their dissimilarity matrix.
• chooseK_mds selects the number of features to be extracted by cross-validation.

seqs <- seq_gen(100)
K_res <- chooseK_mds(seqs, K_cand=5:10, return_dist=TRUE)
theta <- seq2feature_mds(K_res$dist_mat, K_res$K)$theta

seq2seq AE

Similar to MDS, the seq2seq AE method is implemented by two functions. Both functions depend on keras.

• seq2feature_seq2seq extracts K features from a given set of response processes.
• chooseK_seq2seq selects the number of features to be extracted by cross-validation.

seqs <- seq_gen(100)
K_res <- chooseK_seq2seq(seqs, K_cand=c(5, 10), valid_prop=0.2)
seq2seq_res <- seq2feature_seq2seq(seqs, K_res$K, samples_train=1:80, samples_valid=81:100)
theta <- seq2seq_res$theta

Note that if the number of candidates of K is large and a large number of epochs is needed for training the seq2seq AE, chooseK_seq2seq can be slow. One can parallel the selection procedure via multiple independent calls of seq2feature_seq2seq with properly specified training, validation, and test sets.

Sequence Models

A sequence model relates response processes and covariates with a response variable. The model combines a recurrent neural network and a fully connected neural network.

• seqm fits a sequence model. It returns an object of class `seqm'.
• predict.seqm predicts the response variable with a given fitted sequence model. Both seqm and predict.seqm depends on keras.

n <- 100
seqs <- seq_gen(n)
y1 <- sapply(seqs$action_seqs, function(x) "CHECK_A" %in% x)
y2 <- sapply(seqs$action_seqs, function(x) log10(length(x)))

index_test <- sample(1:n, 10)
index_train <- setdiff(1:n, index_test)
seqs_train <- sub_seqs(seqs, index_train)
seqs_test <- sub_seqs(seqs, index_test)

actions <- unique(unlist(seqs))

# a simple sequence model for a binary response variable
seqm_res1 <- seqm(seqs = seqs_train, response = y1, response_type = "binary",
             actions=actions, K_emb = 5, K_rnn = 5, n_epoch = 5)
pred_res1 <- predict(seqm_res1, new_seqs = seqs_test)

# a simple sequence model for a numeric response variable
seqm_res2 <- seqm(seqs = seqs_test, response = y2, response_type = "scale",
             actions=actions, K_emb = 5, K_rnn = 5, n_epoch = 5)
pred_res2 <- predict(seqm_res2, new_seqs = seqs_test)