polynomials: Results of a visual inference study on reading residual plots...

In TengMCing/visage: Visual Inference for Linear Regression Diagnostics

Results of a visual inference study on reading residual plots of misspecified linear regression model caused by missing Hermite polynomial terms

Description

A dataset containing the information of 160 subject and their responses to 588 linupes. There are a total of 588 lineups, where lineup 577 - 588 are used as attention checks. Every subject evaluates 18 different lineups and two randomly assigned attention checks. Every lineup except those used as attention checks has been evaluated by five different subjects. Every lineup consists of 20 residual plots with one actual residual plot and 19 null residual plots drawn with rotated residuals.

Usage

polynomials

Format

A tibble with 3200 rows and 30 variables:

page

The page number of the study website

response_time

Time spent on a page, in milliseconds (1 second = 1000 milliseconds)

set

The set number or the subject ID

num

The lineup number in a set

selection

Selections made by the subject. Multiple selections are allowed and seperated by "_". "0" means the subject can't tell the difference between plots

num_selection

Number of selections made by the subject

reason

The reason for making the selections provided by the subject

confidence

Level of difference between the selected plots and others provided by the subject

age_group

Age group of the subject

educatoin

Educational background of the subject

pronoun

Preferred pronoun

previous_experience

Previous experience in any research that requires reading data graphs

lineup_id

Lineup ID

type

Type of the model

formula

The main formula of the model

shape

Shape of the Hermite polynomials, please check POLY_MODEL$hermite

x_dist

Distribution of the variable x

include_z

Whether to include variable z in the model

e_dist

Distribution of error term e

e_sigma

The standard deviation of the error term e

name

Name of the model

k

Number of residual plots in a lineup

n

Number of observations in a residual plot

effect_size

Effect size of the actual residual plot

answer

The answer of the lineup

detect

Whether the subject selects the actual residual plot

conventional_p_value

P-value of the conventional test (F-test) by comparing the null model (y ~ x) and the correct model (y ~ x + z)

weigthed_detect

If detect == TRUE, weighted_detect = detect/num_selection. Otherwise, weighted_detect = 0.

prop_detect

Poportion of detection of a lineup. For a lineup, prop_detect = mean(weighted_detect).

Details

To reproduce the models, use poly_model().

For x_dist = "uniform", define x = rand_uniform(-1, 1).

For x_dist = "normal", define x = {stand_dist <- function(x) {(x - min(x))/max(x - min(x)) * 2 - 1}; raw_x <- rand_normal(sigma = 0.3); closed_form(~stand_dist(raw_x))}.

For x_dist = "lognormal", define x = {stand_dist <- function(x) {(x - min(x))/max(x - min(x)) * 2 - 1}; raw_x <- rand_lognormal(sigma = 0.6); closed_form(~stand_dist(raw_x/3 - 1))}.

For x_dist = "uniform_discrete", define x = rand_uniform_d(k = 5, even = TRUE).

For example, if shape = 1, e_sigma = 1, include_z = TRUE and x_dist = "uniform", then the model can be defined as y = poly_model(shape = 1, sigma = 1, include_z = TRUE, x = rand_uniform(-1, 1)).

Note that the models will not produce exactly the same lineups as shown to subjects due to randomness. Data stored in get_polynomials_lineup() should be used instead.

TengMCing/visage documentation built on Aug. 28, 2024, 3:27 p.m.