exp3_analysis_supplementary.Rmd

---
title: 'Experiment 3: Supplementary Analyses'
date: "`r Sys.Date()`"
output: 
  github_document:
    toc: true
    toc_depth: 3
  pdf_document:
    toc: true
    toc_depth: 3
editor_options: 
  markdown: 
    wrap: 72
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
options(dplyr.summarise.inform = FALSE)
library(magrittr)
library(lme4)
library(lmerTest)
library(buildmer)
library(kableExtra)
library(ggtext)
library(broom.mixed)
```

# Setup

Variable names:

-   Experiment: exp3\_
-   Data (\_d\_)
    -   d = main df
-   Models (\_m\_)
    -   FF = dummy coded with First + Full Name conditions as 0, Last
        Name condition as 1
    -   L = dummy coded with Last Name condition as 0, First + Full Name
        conditions as 1
    -   quad = quadratic effect of Name Gender
    -   subjGender = participant gender
    -   recenter= center name gender rating by scale (at 4)
-   Plots (\_p\_)

Load data and select columns used in model. See data/exp3_data_about.txt
for more details.

```{r load-data}
exp3_d <- read.csv("../data/exp3_data.csv", stringsAsFactors = TRUE) %>%
  rename("Participant" = "SubjID", "Item" = "Name") %>%
  select(
    Participant, SubjGenderMale, Condition,
    GenderRating, Item, He, She, Other
  )

str(exp3_d)
```

Center gender rating for names: Original scale from 1 to 7, with 1 as
most masculine and 7 as most feminine. Mean-centered with higher still
as more feminine.

```{r center-gender-rating}
exp3_d %<>% mutate(GenderRatingCentered = scale(GenderRating, scale = FALSE))
```

Set contrasts for name conditions. This uses Scott Fraundorf's function
for weighted contrasts. (The psycholing package version doesn't support
doing 2v1 comparisons, only 1v1.) Condition1 is Last vs First+Full.
Condition2 is First vs Full.

```{r contrast-coding}
source("centerfactor.R")
contrasts(exp3_d$Condition) <- centerfactor(
  exp3_d$Condition, c("last", "first")
)
contrasts(exp3_d$Condition)
```

# Quadratic Name Gender Rating

The second supplementary analysis tested the quadratic effect of name
gender rating, such that larger values meant names with stronger gender
associations (masc or fem), and smaller values meant names with weaker
gender associations.

```{r squared-gender-rating}
exp3_d %<>% mutate(GenderRatingSquared = GenderRatingCentered^2)
```

## Model

Quadratic name gender effect on the likelihood of *she* responses, as
opposed to *he* and *other* responses. The maximal model includes random
intercepts by item, but not by participant.

```{r model-quad}
exp3_m_quad <- buildmer(
  formula = She ~ Condition * GenderRatingCentered +
    Condition * GenderRatingSquared +
    (1 | Participant) + (1 | Item),
  data = exp3_d, family = binomial,
  buildmerControl(direction = "order", quiet = TRUE)
)
summary(exp3_m_quad)
```

## Main quadratic effect

To make this easier to understand, plot the data converted to log odds.
This includes just what the model is testing: *she* responses, no
effects of Condition included yet.

```{r plot-quad-main, warning=FALSE}
exp3_p_log <- exp3_d %>%
  group_by(GenderRatingCentered, Item) %>%
  summarise(She.Mean = mean(She)) %>%
  mutate(She.Log = log(She.Mean)) %>%
  ggplot(aes(x = GenderRatingCentered, y = She.Log)) +
  geom_smooth(fill = "red", color = "red") +
  geom_point(fill = "red", color = "red") +
  theme_classic() +
  labs(
    title = "Experiment 3: Log Odds of *She* Responses",
    x = "Masculine - Feminine",
    y = "Log Odds (Item Means)"
  ) +
  theme(
    text = element_text(size = 16),
    plot.title = element_markdown()
  )
exp3_p_log
```

At the masculine end of the scale, *she* responses decrease more
linearly. At the feminine end of the scale, *she* responses level off at
around 5.5 (mostly feminine), then don't ever reach 0. Fewer *she*
responses in 6-7 range than *he* responses in 1-2 range.

## Quadratic interaction

Now, plot the comparison for the Last vs First+Full condition
interaction.

```{r plot-quad-condition, warning=FALSE}
exp3_p_quadCond <- exp3_d %>%
  mutate(Condition_Model = case_when(
    Condition == "first" ~ "First + Full",
    Condition == "full"  ~ "First + Full",
    Condition == "last"  ~ "Last"
  )) %>%
  group_by(Condition_Model, Item, GenderRatingCentered) %>%
  summarise(She.Mean = mean(She)) %>%
  mutate(She.Log = log(She.Mean)) %>%
  ggplot(aes(x = GenderRatingCentered, y = She.Log)) +
  geom_smooth(fill = "red", color = "red") +
  geom_point(fill = "red", color = "red") +
  theme_classic() +
  labs(
    title = "Experiment 3: Log Odds of *She* Responses",
    x = "Masculine - Feminine",
    y = "Log Odds (Item Means)"
  ) +
  theme(
    text = element_text(size = 16),
    plot.title = element_markdown()
  )
exp3_p_quadCond
```

Dummy code to get the quadratic effect just for First and Full Name
conditions.

```{r model-quad-FF}
exp3_d %<>% mutate(Condition_FF = case_when(
  Condition == "first" ~ 0,
  Condition == "full"  ~ 0,
  Condition == "last"  ~ 1
))
exp3_d$Condition_FF %<>% as.factor()

exp3_m_FF_quad <- glmer(
  She ~ 1 + GenderRatingCentered + GenderRatingSquared +
    Condition_FF + GenderRatingCentered:Condition_FF +
    GenderRatingSquared:Condition_FF + (1 | Participant) + (1 | Item),
  data = exp3_d, family = binomial
)

summary(exp3_m_FF_quad)
```

Dummy code to get the quadratic effect just for Last Name condition.

```{r model-quad-L}
exp3_d %<>% mutate(Condition_Last = case_when(
  Condition == "first" ~ 1,
  Condition == "full"  ~ 1,
  Condition == "last"  ~ 0
))
exp3_d$Condition_Last %<>% as.factor()

exp3_m_L_quad <- glmer(
  She ~ 1 + GenderRatingCentered + GenderRatingSquared +
    Condition_Last + GenderRatingCentered:Condition_Last +
    GenderRatingSquared:Condition_Last + (1 | Participant) + (1 | Item),
  data = exp3_d, family = binomial
)
summary(exp3_m_L_quad)
```

```{r OR-quad}
exp3_m_FF_quad %>%
  tidy() %>%
  filter(term == "GenderRatingSquared") %>%
  pull(estimate)

exp3_m_L_quad %>%
  tidy() %>%
  filter(term == "GenderRatingSquared") %>%
  pull(estimate)
```

-   Beta for quadratic gender rating in First + Full: -0.15\*\*\*

-   Beta for quadratic gender rating in Last: -0.05508 .

# Participant Gender

## Setup/Data Summary

The third supplementary analysis looks at participant gender: if male
participants show a larger bias towards *he* responses than non-male
participants.

Participants entered their gender in a free-response box.

```{r count-subjGender}
exp3_d %>%
  group_by(SubjGenderMale) %>%
  summarise(total = n_distinct(Participant)) %>%
  kable()
```

For this analysis, we exclude participants who did not respond (N=116)..
Because there are not enough participants to create 3 groups, we compare
male to non-male participants. Male participants (N=514) are coded as 1
and female (N=638), nonbinary (N=2), agender (N=1), and asexual (N=1)
participants are coded as 0.

Summary of responses by condition and participant gender:

```{r means-subjGender}
exp3_d_subjGender <- exp3_d %>% filter(!is.na(SubjGenderMale))
exp3_d_subjGender %<>% mutate(ResponseAll = case_when(
  He    == 1 ~ "He",
  She   == 1 ~ "She",
  Other == 1 ~ "Other"
))
```

Participant gender is mean centered effects coded, comparing non-male
participants to male participants.

```{r contrast-coding-subj-gender}
exp3_d_subjGender$SubjGenderMale %<>% as.factor()
contrasts(exp3_d_subjGender$SubjGenderMale) <- cbind("NM_M" = c(-.5, .5))
contrasts(exp3_d_subjGender$SubjGenderMale)
```

## Model

Effects of Name Condition (first name, full name), the first name's
Gender Rating (centered, positive=more feminine), and Participant Gender
(non-male vs. male) on the likelihood of a *she* response as opposed to
*he* or *other* responses. The maximal model contains random intercepts
by item and by participant.

```{r model-subj-gender}
exp3_m_subjGender <- buildmer(
  formula = She ~ Condition * GenderRatingCentered * SubjGenderMale +
    (1 | Participant) + (1 | Item),
  data = exp3_d_subjGender, family = binomial,
  buildmerControl(direction = "order", quiet = TRUE)
)

summary(exp3_m_subjGender)
```

-   Male participants less likely to produce *she* responses overall

-   No interactions with participant gender significant

# Gender Rating Centering

The first name gender ratings aren't perfectly centered, partially
because mostly-feminine/somewhat-masculine names are much less common
than mostly-masculine/somewhat-feminine names.

```{r gender-rating-mean-center}
mean(exp3_d$GenderRating, na.rm = TRUE)
```

Does it make a difference if we center it on 4, the mean of the scale,
instead of 4.21, the mean of the items?

```{r gender-rating-abs-center}
exp3_d %<>% mutate(GenderRating4 = GenderRating - 4)
```

```{r model-gender-rating-recenter}
exp3_m_recenter <- glmer(
  She ~ Condition * GenderRating4 + (1 | Participant) + (1 | Item),
  exp3_d,
  family = binomial
)
summary(exp3_m_recenter)
```

Here, the beta estimate for the intercept has a larger absolute value
(-1.76 vs -1.52), and the beta estimates for the condition effects is
slightly different (0.13 vs 0.15; 0.10 vs 0.09).