exp2_analysis_supplementary.Rmd

---
title: 'Experiment 2: 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(broom.mixed)
library(insight)
library(kableExtra)
```

# Setup

Variable names:

-   Experiment: exp2\_

-   Data (\_d\_)

    -   d = main df
    -   FF = First + Full Name conditions only
    -   noOther = just *he* and *she* responses
    -   subjGender = participant gender

-   Models (\_m\_)

    -   cond = effect of Condition (Last vs First+Full)
    -   nameGender = effects of Condition (First vs Full) and Name
        Gender Rating
    -   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 Gender Rating
    -   subjGender = participant gender
    -   recentered = center name gender rating by scale (at 4)

Load data and select columns used in model. See data/exp2_data_about.txt
for more details.

```{r load-data}
exp2_d <- read.csv("../data/exp2_data.csv",
                   stringsAsFactors = TRUE) %>%
  rename("Participant" = "SubjID", "Item" = "NameShown") %>%
  select(
    Participant, SubjGenderMale, Condition, GenderRating,
    Item, Male, Female, Other
  )
str(exp2_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}
exp2_d %<>% mutate(GenderRatingCentered = scale(GenderRating, scale = FALSE))
```

Set contrasts for name conditions.

```{r contrast-coding}
contrasts(exp2_d$Condition) <- cbind(
  "last vs first/full" = c(.33, .33, -0.66),
  "first vs full"      = c(-.5, .5, 0)
)
contrasts(exp2_d$Condition)
```

Subset for gender rating effects (First and Full conditions only).

```{r subset-FF}
exp2_d_FF <- exp2_d %>% filter(Condition != "last")
exp2_d_FF$Condition %<>% droplevels()

contrasts(exp2_d_FF$Condition) <- cbind(
  "first vs full" = c(-.5, .5)
) # add contrast back
contrasts(exp2_d_FF$Condition)
```

# Without *Other* Responses

The first supplementary analysis tests if excluding OTHER responses
(3.72% of total responses) affects the pattern of results.

```{r count-other}
sum(exp2_d$Other)
sum(exp2_d$Other) / length(exp2_d$Other)
```

Exclude *other* responses.

```{r subset-other}
exp2_d_noOther <- exp2_d %>% filter(Other == 0)
exp2_d_FF_noOther <- exp2_d_FF %>% filter(Other == 0)
```

## Model 1: Condition w/o *Other* Responses

Effect of Name Condition (first name, last name, full name) on
likelihood of a *female* response, as opposed to a *male* response, with
*other* responses excluded. Participant and Item are again included as
random intercepts, with items defined as the unique first, last and
first + last name combinations.

```{r model-condition-other}
exp2_m_cond_noOther <- glmer(
  Female ~ Condition + (1 | Participant) + (1 | Item),
  data = exp2_d_noOther, family = binomial
)
summary(exp2_m_cond_noOther)
```

No differences.

### Odds Ratios: Intercept

```{r OR-condiiton-other}
exp(get_intercept(exp2_m_cond_noOther))
exp(-get_intercept(exp2_m_cond_noOther))
```

0.45x less likely to recall as female overall (or: 2.19x more likely to
recall as male/other overall), p\<.001

### Odds Ratios: Last vs First+Full

```{r OR-LFF-other}
exp2_m_cond_noOther %>%
  tidy() %>%
  filter(term == "Conditionlast vs first/full") %>%
  pull(estimate) %>%
  exp()
```

6.84x more likely to use *she* in First + Full compared to Last (or:
6.84x times more likely to use *he* and *other* in Last than in First +
Full), p\<.001

### Odds Ratios: Last Only

Dummy code with Last Name as 0, so that intercept is the Last Name
condition only.

```{r dummy-code-L-other}
exp2_d_noOther %<>% mutate(Condition_Last = case_when(
  Condition == "first" ~ 1,
  Condition == "full"  ~ 1,
  Condition == "last"  ~ 0
))
exp2_d_noOther$Condition_Last %<>% as.factor()
```

```{r model-L-other}
exp2_m_L_noOther <- glmer(
  Female ~ Condition_Last + (1 | Participant) + (1 | Item),
  data = exp2_d_noOther, family = binomial
)
summary(exp2_m_L_noOther)
```

```{r OR-L-other}
exp(get_intercept(exp2_m_L_noOther))
exp(-get_intercept(exp2_m_L_noOther))
```

0.13x times less likely to recall as female in the Last Name condition
(or: 7.80x more likely to recall as male in the Last Name condition),
p\<.001

### Odds Ratios: First and Full Only

Dummy code with First and Full Name as 0, so that intercept is average
for these two conditions.

```{r dummy-code-FF-other}
exp2_d_noOther %<>% mutate(Condition_FF = case_when(
  Condition == "first" ~ 0,
  Condition == "full"  ~ 0,
  Condition == "last"  ~ 1
))
exp2_d_noOther$Condition_FF %<>% as.factor()
```

```{r model-FF-other}
exp2_m_FF_noOther <- glmer(
  Female ~ Condition_FF + (1 | Participant) + (1 | Item),
  data = exp2_d_noOther, family = binomial
)
summary(exp2_m_FF_noOther)
```

```{r OR-FF-other}
exp(get_intercept(exp2_m_FF_noOther))
exp(-get_intercept(exp2_m_FF_noOther))
```

0.82x times less likely o recall as female in the First and Full Name
conditions (or: 1.22x more likely to use *he* in the n the First and
Full Name conditions), p=.17

## Model 2: Condition \* Name Gender w/o *Other* Responses

Effects of Name Condition (first name, full name) and the first name's
Gender Rating (centered, positive=more feminine) on the likelihood of a
*female* response as opposed to a *male* response, with *other*
responses excluded. In Experiment 2, the Last Name condition does not
include any instances of the gendered first name, so it is not included
here. Participant and Item are again included as random intercepts.

```{r model-gender-rating-other}
exp2_m_nameGender_noOther <- glmer(
  Female ~ Condition * GenderRatingCentered + (1 | Participant) + (1 | Item),
  data = exp2_d_FF_noOther, family = binomial
)
summary(exp2_m_nameGender_noOther)
```

Compared to the main analysis including *other* responses, the intercept
has a larger p-value, the difference between the First and Full Name
conditions is no longer trending, and the Name Gender Rating is the
same.

# Quadratic Name Gender Rating

The second supplementary analysis tested the effect of squared 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}
exp2_d_FF %<>% mutate(GenderRatingSquared = GenderRatingCentered^2)
```

## Model 3: Quadratic

No quadratic effects.

```{r model-quad}
exp2_m_nameGender_quad <- glmer(
  Female ~ Condition * GenderRatingCentered + Condition * GenderRatingSquared +
    (1 | Participant) + (1 | Item),
  data = exp2_d_FF, family = binomial
)
summary(exp2_m_nameGender_quad)
```

# Participant Gender

## Setup/Data Summary

The third supplementary analysis looks at participant gender: if male
participants show a larger bias to recall the character as male than
non-male participants.

Participants entered their gender in a free-response box.

```{r count-subjGender}
exp2_d %>%
  group_by(SubjGenderMale) %>%
  summarise(total = n_distinct(Participant)) %>%
  kable()
```

For this analysis, we exclude participants who did not respond (N=88).
Because there are not enough participants to create 3 groups, we compare
male to non-male participants. Male participants (N=694) are coded as 1,
and female (N=566), nonbinary (N=2), and genderqueer (N=1) participants
are coded as 0.

Summary of responses by condition and participant gender:

```{r means-subj-gender}
exp2_d_subjGender <- exp2_d %>%
  filter(!is.na(SubjGenderMale)) %>%
  mutate(ResponseAll = case_when(
    Male   == 1 ~ "Male",
    Female == 1 ~ "Female",
    Other  == 1 ~ "Other"
  ))

exp2_d_subjGender %>%
  group_by(Condition, ResponseAll, SubjGenderMale) %>%
  summarise(n = n()) %>%
  pivot_wider(
    names_from = ResponseAll,
    values_from = n
  ) %>%
  rename("ParticipantGender" = "SubjGenderMale") %>%
  mutate(ParticipantGender = case_when(
    ParticipantGender == "0" ~ "Non-male",
    ParticipantGender == "1" ~ "Male"
  )) %>%
  mutate(
    Female_MaleOther = Female / (Male + Other),
    Female_Male = Female / Male
  ) %>%
  kable(digits = 3)
```

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

```{r contrast-coding-subj-gender}
exp2_d_subjGender$SubjGenderMale %<>% as.factor()
contrasts(exp2_d_subjGender$SubjGenderMale) <- cbind("NM_M" = c(-.5, .5))
contrasts(exp2_d_subjGender$SubjGenderMale)
```

Subset First and Full conditions.

```{r subset-FF-subj-gender}
exp2_d_FF_subjGender <- exp2_d_subjGender %>% filter(Condition != "last")
exp2_d_FF_subjGender$Condition %<>% droplevels()

contrasts(exp2_d_FF_subjGender$Condition) <-
  cbind("first vs full" = c(-.5, .5)) # add contrast back
contrasts(exp2_d_FF_subjGender$Condition)
```

## Model 4: Condition \* Participant Gender

Effect of Name Condition (first name, last name, full name) and
Participant Gender (non-male vs male) on likelihood of a *female*
response, as opposed to a *male* response or *other* response.
Participant and Item are again included as random intercepts.

```{r model-condition-subj-gender}
exp2_m_cond_subjGender <- glmer(
  Female ~ Condition * SubjGenderMale + (1 | Participant) + (1 | Item),
  data = exp2_d_subjGender, family = binomial
)
summary(exp2_m_cond_subjGender)
```

-   Male participants are less likely to recall the character as female
    overall, but this is not significant after correction for multiple
    comparisons.

-   The interaction between Condition (Last vs. First + Full) and
    Participant Gender is significant.

### Interaction

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

```{r model-FF-subj-gender}
exp2_d_subjGender %<>% mutate(Condition_FF = case_when(
  Condition == "first" ~ 0,
  Condition == "full"  ~ 0,
  Condition == "last"  ~ 1
))
exp2_d_subjGender$Condition_FF %<>% as.factor()

exp2_m_cond_FF_subjGender <- glmer(
  Female ~ Condition_FF * SubjGenderMale + (1 | Participant) + (1 | Item),
  data = exp2_d_subjGender, family = binomial
)
summary(exp2_m_cond_FF_subjGender)
```

Then dummy code to get the participant gender effect just for Last Name
condition.

```{r model-L-subj-gender}
exp2_d_subjGender %<>% mutate(Condition_L = case_when(
  Condition == "first" ~ 1,
  Condition == "full"  ~ 1,
  Condition == "last"  ~ 0
))
exp2_d_subjGender$Condition_L %<>% as.factor()

exp2_m_cond_L_subjGender <- glmer(
  Female ~ Condition_L * SubjGenderMale + (1 | Participant) + (1 | Item),
  data = exp2_d_subjGender, family = binomial
)
summary(exp2_m_cond_L_subjGender)
```

-   Beta for subj gender in First + Full: -0.26325
-   Beta for subj gender in Last: 0.1505 NS

--\> Male participants were less likely to recall the referent as female
than non-male participants in the First and Full Name conditions. No
participant gender difference in the Last Name condition.

## Model 5: Condition \* Name Gender \* Participant Gender

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 *female* response as opposed
to *male* or *other* responses. In Experiment 2, the Last Name condition
does not include any instances of the gendered first name, so it is not
included here.

```{r model-gender-rating-subj-gender}
exp2_m_nameGender_subjgender <- buildmer(
  formula = Female ~ Condition * GenderRatingCentered * SubjGenderMale +
    (1 | Participant) + (1 | Item),
  data = exp2_d_FF_subjGender, family = binomial,
  buildmerControl(direction = "order", quiet = TRUE)
)
summary(exp2_m_nameGender_subjgender)
```

-   Male participants are less likely to recall the character as female
    overall. This matches the results of the interaction in the
    condition-only model.
-   The interaction between participant gender and first name gender
    rating is significant. Smaller effect of name gender rating in male
    participants.
-   Interaction with Condition, three-way interaction with Name Gender
    and Condition n.s.

# 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(exp2_d$GenderRating, na.rm = TRUE)
```

Does it make a difference if we center it on 4, the mean of the scale,
instead of 4.22, the mean of the items?

```{r gender-rating-abs-center}
exp2_d_FF %<>% mutate(GenderRating4 = GenderRating - 4)
```

## Model 6: Gender Rating Recentered

```{r model-gender-rating-recenter}
exp2_m_recenter <- glmer(
  Female ~ Condition * GenderRating4 + (1 | Participant) + (1 | Item),
  data = exp2_d_FF, family = binomial
)
summary(exp2_m_recenter)
```

Here, the absolute value of the beta estimate for the intercept is again
larger for the intercept (-0.35 vs -0.18) but the same for the condition
effect (-0.21 vs -0.22).