Type:	Package
Title:	Calculating the M2 Model Fit Statistic for Diagnostic Classification Models
Version:	1.0.2
Description:	A collection of functions for calculating the M2 model fit statistic for diagnostic classification models as described by Liu et al. (2016) <doi:10.3102/1076998615621293>. These functions provide multiple sources of information for model fit according to the M2 statistic, including the M2 statistic, the *p* value for that M2 statistic, and the Root Mean Square Error of Approximation based on the M2 statistic.
License:	GPL-3
URL:	https://github.com/atlas-aai/dcm2
BugReports:	https://github.com/atlas-aai/dcm2/issues
Depends:	R (≥ 3.6)
Imports:	dplyr (≥ 0.8.4), glue (≥ 1.4.2), magrittr (≥ 1.5), methods (≥ 4.1.0), modelr (≥ 0.1.8), purrr (≥ 0.3.3), Rcpp, rlang (≥ 0.4.11), stringr (≥ 1.4.0), tibble (≥ 2.1.3), tidyr (≥ 1.1.4)
Suggests:	covr, GDINA, roxygen2, spelling, testthat (≥ 2.1.0)
LinkingTo:	Rcpp, RcppArmadillo (≥ 0.9.800.1.0)
Config/testthat/edition:	3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.3
Language:	en-US
NeedsCompilation:	yes
Packaged:	2023-03-20 19:54:01 UTC; jeff
Author:	Jeffrey Hoover [aut, cre, cph], W. Jake Thompson [aut], Wenchao Ma [ctb] (Author of Mord.cpp)
Maintainer:	Jeffrey Hoover <jeffrey.c.hoover@gmail.com>
Repository:	CRAN
Date/Publication:	2023-03-21 19:50:02 UTC

dcm2: A package for the estimating the M2 statistic for DCMs

Description

A collection of functions for calculating the M2 model fit statistic for diagnostic classification models as described by Liu et al. (2016) doi: 10.3102/1076998615621293. These functions provide multiple sources of information for model fit according to the M2 statistic, including the M2 statistic, the *p* value for that M2 statistic, and the Root Mean Square Error of Approximation based on the M2 statistic.

Author(s)

Maintainer: Jeffrey Hoover jeffrey.c.hoover@gmail.com (ORCID) [copyright holder]

Authors:

• W. Jake Thompson wjakethompson@gmail.com (ORCID)

Other contributors:

• Wenchao Ma wenchao.ma@ua.edu (Author of Mord.cpp) [contributor]

See Also

Useful links:

• https://github.com/atlas-aai/dcm2

• Report bugs at https://github.com/atlas-aai/dcm2/issues

Pipe operator

Description

See ⁠magrittr::[\%>\%][magrittr::\%>\%]⁠ for details.

Usage

lhs %>% rhs

Value

No return value, called to import pipe operator from magrittr

Make Binary Profiles

Description

Given a number of attributes, as_binary will create all possible binary mastery profiles.

Usage

as_binary(x)

Arguments

Value

A 2 ^ x by x matrix

Examples

as_binary(3)
as_binary(4)

Calculate the M2

Description

Calculate the M2

Usage

calc_m2(
  data,
  struc_params,
  pi_matrix,
  qmatrix,
  ci = 0.9,
  link = "logit",
  model_type = c("LCDM", "GDINA", "ACDM", "LLM", "RRUM", "DINO", "DINA", "BUGDINO")
)

Arguments

Value

A data frame containing:

• m2: The M2 statistic

• df: Degrees of freedom for the M2 statistic

• pval: p-value for the M2 statistic

• rmsea: Root mean square error of approximation

• ci_lower: Lower end of ci interval for RMSEA

• ci_upper: Upper end of ci interval for RMSEA

• srmsr: Standardized root mean square residual

Examples

possible_prof <- dcm2::as_binary(ncol(sample_data$q_matrix))

fit_dat <- sample_data$data %>%
             tidyr::pivot_wider(names_from = "item_id",
                                values_from = "score") %>%
             dplyr::select(-"resp_id") %>%
             as.matrix() %>%
             unname()
gdina_mod <- GDINA::GDINA(dat = fit_dat,
                          Q = data.frame(sample_data$q_matrix),
                          model = "logitGDINA",
                          control = list(conv.type = "neg2LL"))
struc_params <- gdina_mod$struc.parm
pi_matrix <- gdina_mod$LC.prob %>%
               as.matrix() %>%
               unname()
calc_m2(data = fit_dat, struc_params, pi_matrix,
        qmatrix = data.frame(sample_data$q_matrix), ci = 0.9, link = "logit",
        model_type = "LCDM")

Simulated Data for a Single Attribute Assessment

Description

A list containing data from a randomly simulated single-attribute assessment.

Usage

data_att1

Format

A list frame containing 4 tibble objects:

• resp_profiles: A tibble with 1000 rows and 2 columns. The first column indicates resp_id (i.e., the respondent identification number) and the second column indicates att_1 (i.e., a binary indicator for whether the respondent mastered the first attribute).

• q_matrix: A tibble with 2 rows and 1 column. Each row corresponds to an assessment item, and the column entries provide a binary indicator for whether the item assessed the attribute.

• item_params: A tibble with 2 rows and 3 columns. Each row corresponds to an item. The first column indicates item_id (i.e., the item identification number). The second column indicates intercept (i.e., the true item intercept parameter for the item). The third column indicates att_1 (i.e., the true item main effect parameter for the item).

• data: A tibble with 2000 rows and 3 columns. The first column indicates resp_id (i.e., the respondent identification number). The second column indicates item_id (i.e., the item identification number). The third column indicates score (i.e., the dichotomously scored item response).

Model Fit M2 Calculations

Description

Estimate the M2 statistic as described by Liu et al. (2016).

Usage

fit_m2(model, ci = 0.9, ...)

Arguments

Value

A data frame containing:

• m2: The M2 statistic

• df: Degrees of freedom for the M2 statistic

• pval: p-value for the M2 statistic

• rmsea: Root mean square error of approximation

• ci_lower: Lower end of ci interval for RMSEA

• ci_upper: Upper end of ci interval for RMSEA

• srmsr: Standardized root mean square residual

References

Liu, Y., Tian, W., & Xin, T. (2016). An application of M_2 statistic to evaluate the fit of cognitive diagnostic models. Journal of Educational and Behavioral Statistics, 41, 3-26. doi: 10.3102/1076998615621293

Examples

possible_prof <- dcm2::as_binary(ncol(sample_data$q_matrix))

fit_dat <- sample_data$data %>%
             tidyr::pivot_wider(names_from = "item_id",
                                values_from = "score") %>%
             dplyr::select(-"resp_id") %>%
             as.matrix() %>%
             unname()
gdina_mod <- GDINA::GDINA(dat = fit_dat,
                          Q = data.frame(sample_data$q_matrix),
                          model = "logitGDINA",
                          control = list(conv.type = "neg2LL"))
fit_m2(gdina_mod, ci = 0.9)

Log-odds Transformation

Description

These functions implement the log-odds (or logit) transformation. This is a common transformation for psychometric models that is used to put probabilities on a continuous scale.

Usage

logit(x)

inv_logit(x)

Arguments

Value

A transformed double

Examples

logit(0.6)
logit(0.5)

inv_logit(3.5)
inv_logit(0)

Simulated Data for Testing Functions

Description

A matrix with randomly simulated data to test the package functions.

Usage

sample_data

Format

A list frame containing 4 tibble objects:

• resp_profiles: A tibble with 1000 rows and 3 columns. The first column indicates resp_id (i.e., the respondent identification number). The second column indicates att_1 (i.e., a binary indicator for whether the respondent mastered the first attribute). The third column indicates att_2 (i.e., a binary indicator for whether the respondent mastered the second attribute).

• q_matrix: A tibble with 8 rows and 2 columns. Each row corresponds to an assessment item, and the column entries provide a binary indicator for whether the item assessed each of the attribute.

• item_params: A tibble with 8 rows and 5 columns. Each row corresponds to an item. The first column indicates item_id (i.e., the item identification number). The second column indicates intercept (i.e., the true item intercept parameter for the item). The third column indicates att_1 (i.e., the true item main effect parameter for the first attribute for the item). The fourth column indicates att_2 (i.e., the true item main effect parameter for the second attribute for the item). The fifth column indicates att_1__att_2 (i.e., the true item interaction effect parameter for the first and second attributes).

• data: A tibble with 8000 rows and 3 columns. The first column indicates resp_id (i.e., the respondent identification number). The second column indicates item_id (i.e., the item identification number). The third column indicates score (i.e., the dichotomously scored item response).

Tidy eval helpers

Description

This page lists the tidy eval tools reexported in this package from rlang. To learn about using tidy eval in scripts and packages at a high level, see the dplyr programming vignette and the ggplot2 in packages vignette. The Metaprogramming section of Advanced R may also be useful for a deeper dive.

• The tidy eval operators ⁠{{⁠, ⁠!!⁠, and ⁠!!!⁠ are syntactic constructs which are specially interpreted by tidy eval functions. You will mostly need ⁠{{⁠, as ⁠!!⁠ and ⁠!!!⁠ are more advanced operators which you should not have to use in simple cases.

  The curly-curly operator ⁠{{⁠ allows you to tunnel data-variables passed from function arguments inside other tidy eval functions. ⁠{{⁠ is designed for individual arguments. To pass multiple arguments contained in dots, use ... in the normal way.

  my_function <- function(data, var, ...) {
    data %>%
      group_by(...) %>%
      summarise(mean = mean({{ var }}))
  }
  

• enquo() and enquos() delay the execution of one or several function arguments. The former returns a single expression, the latter returns a list of expressions. Once defused, expressions will no longer evaluate on their own. They must be injected back into an evaluation context with ⁠!!⁠ (for a single expression) and ⁠!!!⁠ (for a list of expressions).

  my_function <- function(data, var, ...) {
    # Defuse
    var <- enquo(var)
    dots <- enquos(...)
  
    # Inject
    data %>%
      group_by(!!!dots) %>%
      summarise(mean = mean(!!var))
  }
  

  In this simple case, the code is equivalent to the usage of ⁠{{⁠ and ... above. Defusing with enquo() or enquos() is only needed in more complex cases, for instance if you need to inspect or modify the expressions in some way.

• The .data pronoun is an object that represents the current slice of data. If you have a variable name in a string, use the .data pronoun to subset that variable with [[.

  my_var <- "disp"
  mtcars %>% summarise(mean = mean(.data[[my_var]]))
  

• Another tidy eval operator is ⁠:=⁠. It makes it possible to use glue and curly-curly syntax on the LHS of =. For technical reasons, the R language doesn't support complex expressions on the left of =, so we use ⁠:=⁠ as a workaround.

  my_function <- function(data, var, suffix = "foo") {
    # Use `{{` to tunnel function arguments and the usual glue
    # operator `{` to interpolate plain strings.
    data %>%
      summarise("{{ var }}_mean_{suffix}" := mean({{ var }}))
  }
  

• Many tidy eval functions like dplyr::mutate() or dplyr::summarise() give an automatic name to unnamed inputs. If you need to create the same sort of automatic names by yourself, use as_label(). For instance, the glue-tunnelling syntax above can be reproduced manually with:

  my_function <- function(data, var, suffix = "foo") {
    var <- enquo(var)
    prefix <- as_label(var)
    data %>%
      summarise("{prefix}_mean_{suffix}" := mean(!!var))
  }
  

  Expressions defused with enquo() (or tunnelled with ⁠{{⁠) need not be simple column names, they can be arbitrarily complex. as_label() handles those cases gracefully. If your code assumes a simple column name, use as_name() instead. This is safer because it throws an error if the input is not a name as expected.

Value

No return value, called to reexport tools in this package from rlang