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- -YEAR: 2024 -COPYRIGHT HOLDER: Marko Lalovic -- -
YEAR: 2024 -COPYRIGHT HOLDER: Marko Lalovic -- -
Copyright (c) 2024 Marko Lalovic
-Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
-The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
-THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
-
In social sciences, variables of interest are often conceptualized as -latent variables — hidden continuous variables measured through Likert -scale questions, typically categorized as Strongly disagree, Disagree, -Neutral, Agree, and Strongly agree. Researchers frequently aim to -uncover these latent variables using various statistical techniques. -Accurate modeling of survey data is essential for comparative analysis -through simulation. The latent2likert package addresses -this need by providing an effective algorithm to simulate Likert -response variables from hypothetical latent variables. This vignette -provides two practical workflow examples demonstrating the use of the -latent2likert package.
-The following hypothetical survey simulation is loosely based on an -actual comparative study on teaching and learning R in a pair of -introductory statistics labs (McNamara 2024).
-Imagine a situation where 10 participants from Course A and 20 -participants from Course B have completed the survey. Suppose the -initial question was:
---“How would you rate your experience with the course?”
-
with four possible answers:
---Poor, Fair, Good, and Excellent.
-
Let’s assume that the participants in Course A were neutral regarding -the question, while participants in Course B had a more positive -experience on average.
-By choosing appropriate parameters for the latent distributions and -setting the number of categories n_levels = 4, we can generate -hypothetical responses (standard deviation sd = 1 and skewness skew = 0, -by default):
-
-library(latent2likert) # Load the package
-set.seed(12345) # Ensure reproducible results
-
-# Generate responses for Course A and Course B
-responses_A <- rlikert(size = 10, n_items = 1, n_levels = 4, mean = 0, sd = 1)
-responses_B <- rlikert(size = 20, n_items = 1, n_levels = 4, mean = 1, sd = 1)To summarize the results, create a data frame from all responses:
-
-n_levels <- 4
-n_groups <- 2
-categories <- c("Poor", "Fair", "Good", "Excellent")
-
-# Create a data frame to summarize the responses
-response_data <- data.frame(
- Course = rep(c("A", "B"), each = n_levels),
- Response = factor(rep(categories, n_groups), levels = categories),
- Proportion = c(
- response_prop(responses_A, n_levels),
- response_prop(responses_B, n_levels)
- )
-)
-
-# Filter out rows with zero proportions
-response_data <- response_data[response_data$Proportion > 0, ]
-response_data
-#> Course Response Proportion
-#> 1 A Poor 0.30
-#> 2 A Fair 0.20
-#> 3 A Good 0.20
-#> 4 A Excellent 0.30
-#> 6 B Fair 0.10
-#> 7 B Good 0.25
-#> 8 B Excellent 0.65The results can then be visualized using a grouped bar chart:
-
Now suppose that the survey also asked the participants to rate their -skills on a 5-point Likert scale, ranging from 1 (very poor) to 5 (very -good) in:
-The survey was completed by the participants both before and after -taking the course for a pre and post-comparison. Suppose that -participants’ assessments of:
-Let’s simulate the survey data for this scenario:
-
-# Pre- and post-assessments of skills for Course A
-pre_A <- rlikert(size = 10, n_items = 3, n_levels = 5, mean = c(-1, 0, 1))
-post_A <- rlikert(size = 10, n_items = 3, n_levels = 5, mean = c(0, 0, 2))
-
-# Pre- and post-assessments of skills for Course B
-pre_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(-1, 0, 1))
-post_B <- rlikert(size = 20, n_items = 3, n_levels = 5, mean = c(0, 0, 0))Create a data frame from all responses to summarize the results:
-
-# Combine pre and post responses into a list
-pre_post <- list(pre_A, post_A, pre_B, post_B)
-
-# Number of items and response levels
-n_items <- 3
-n_levels <- 5
-
-# Define skills assessed
-skills <- c("Programming", "Searching online", "Solving problems")
-
-# Generate repeated skill labels for questions
-questions <- rep(rep(skills, each = n_levels), 4)
-questions <- factor(questions, levels = skills)
-
-# Create a data frame to summarize the responses
-response_data <- data.frame(
- Course = rep(c("Course A", "Course B"), each = 2 * n_items * n_levels),
- Question = questions,
- Time = as.factor(rep(c(
- rep("before", n_items * n_levels),
- rep("after", n_items * n_levels)
- ), 2)),
- Response = rep(seq_len(n_levels), 2 * n_items * 2),
- Proportion = as.vector(sapply(pre_post, function(d) {
- as.vector(t(response_prop(d, n_levels)))
- }))
-)
-
-head(response_data)
-#> Course Question Time Response Proportion
-#> 1 Course A Programming before 1 0.5
-#> 2 Course A Programming before 2 0.2
-#> 3 Course A Programming before 3 0.3
-#> 4 Course A Programming before 4 0.0
-#> 5 Course A Programming before 5 0.0
-#> 6 Course A Searching online before 1 0.1And visualize the results with a stacked bar chart:
-
We will use part of the bfi -data set from (Revelle -2024). Specifically, we’ll focus on the first 5 items -corresponding to agreeableness. To investigate the differences in -agreeableness between men and women, we’ll also use the gender -attribute.
-Load the data:
-
-data(part_bfi)
-head(part_bfi)
-#> A1 A2 A3 A4 A5 gender
-#> 61617 2 4 3 4 4 0
-#> 61618 2 4 5 2 5 1
-#> 61620 5 4 5 4 4 1
-#> 61621 4 4 6 5 5 1
-#> 61622 2 3 3 4 5 0
-#> 61623 6 6 5 6 5 1Separate the items into two groups according to their gender:
-
-vars <- c("A1", "A2", "A3", "A4", "A5")
-items_male <- part_bfi[part_bfi$gender == 0, vars]
-items_female <- part_bfi[part_bfi$gender == 1, vars]Estimate the parameters of the latent variables, assuming they are
-normal and providing the number of possible response categories
-n_levels = 6:
-params_male <- estimate_params(data = items_male, n_levels = 6)
-params_female <- estimate_params(data = items_female, n_levels = 6)Generate new responses to the items using the estimated parameters -and estimated correlations:
-
-set.seed(12345) # Ensure reproducible results
-
-new_items_male <- rlikert(
- size = nrow(items_male),
- n_items = 5,
- n_levels = 6,
- mean = params_male["mean", ],
- sd = params_male["sd", ],
- corr = cor(items_male)
-)
-
-new_items_female <- rlikert(
- size = nrow(items_female),
- n_items = 5,
- n_levels = 6,
- mean = params_female["mean", ],
- sd = params_female["sd", ],
- corr = cor(items_female)
-)Create agreeableness scale scores for both groups of participants by -taking the average of these 5 items:
-
-# Combine new items and gender in new data frame
-new_data <- data.frame(rbind(new_items_male, new_items_female))
-new_data$gender <- c(rep(0, nrow(items_male)), rep(1, nrow(items_female)))
-head(new_data)
-#> Y1 Y2 Y3 Y4 Y5 gender
-#> 1 3 5 5 4 5 0
-#> 2 1 5 4 4 4 0
-#> 3 2 6 5 6 4 0
-#> 4 4 4 4 6 5 0
-#> 5 4 5 3 2 2 0
-#> 6 5 4 5 6 5 0
-
-# Reverse the first item because it has negative correlations
-part_bfi$A1 <- (min(part_bfi$A1) + max(part_bfi$A1)) - part_bfi$A1
-new_data$Y1 <- (min(new_data$Y1) + max(new_data$Y1)) - new_data$Y1
-
-# Create agreeableness scale scores
-part_bfi$agreeable <- rowMeans(part_bfi[, vars])
-new_data$agreeable <- rowMeans(new_data[, c("Y1", "Y2", "Y3", "Y4", "Y5")])The results can be visualized with a grouped boxplot:
-
Marko Lalovic. Author, maintainer. -
-Source: DESCRIPTION
Lalovic M (2024). -latent2likert: Converting Latent Variables into Likert Scale Responses. -R package version 1.2.1, https://lalovic.io/latent2likert/. -
-@Manual{,
- title = {latent2likert: Converting Latent Variables into Likert Scale Responses},
- author = {Marko Lalovic},
- year = {2024},
- note = {R package version 1.2.1},
- url = {https://lalovic.io/latent2likert/},
-}
-