Package 'dcm2'

Make Binary Profiles

Description

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

Usage

as_binary(x)

Arguments

x	The number of attributes

Value

A 2 ^ x by x matrix

Examples

as_binary(3)
as_binary(4)

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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

data	A data frame containing the raw data, where there is one row per respondent and one column per item
struc_params	A vector containing the structural parameters of the estimated model
pi_matrix	An item-by-class matrix containing the probability of a correct response by members of each latent class
qmatrix	A data frame containing the Q-matrix
ci	The confidence interval for the RMSEA, computed from the M2
link	A character containing the link function.
model_type	A character containing the model type (e.g., LCDM) that was estimated.

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")

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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).

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Model Fit M2 Calculations

Description

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

Usage

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

Arguments

model	An estimated diagnostic classification model.
ci	The confidence interval for the RMSEA.
...	Unused, for extensibility.

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)

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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

x	A number to be transformed

Value

A transformed double

Examples

logit(0.6)
logit(0.5)

inv_logit(3.5)
inv_logit(0)

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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).

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