exp1_analysis_supplementary.Rmd

---
title: 'Experiment 1: 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: exp1\_
-   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

    -   recenter = center name Gender Rating by scale (at 4)

Load data and select columns used in model. See data/exp1_data_about.txt
for more details.

```{r load-data}
exp1_d <- read.csv("../data/exp1_data.csv",
                   stringsAsFactors = TRUE) %>%
  rename("Participant" = "SubjID", "Item" = "NameShown") %>%
  select(
    Participant, SubjGenderMale,
    Condition, GenderRating,
    Item, He, She, Other
  )
str(exp1_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}
exp1_d %<>% mutate(GenderRatingCentered = scale(GenderRating, scale = FALSE))
```

Set contrasts for name conditions.

```{r contrast-coding}
contrasts(exp1_d$Condition) <- cbind(
  "last vs first/full" = c(.33, .33, -0.66),
  "first vs full"      = c(-.5, .5, 0)
)
contrasts(exp1_d$Condition)
```

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

```{r subset-FF}
exp1_d_FF <- exp1_d %>% filter(Condition != "last")
exp1_d_FF$Condition %<>% droplevels()

contrasts(exp1_d_FF$Condition) <- cbind(
  "first vs full" = c(-.5, .5)
) # add contrast back
contrasts(exp1_d_FF$Condition)
```

# Without *Other* Responses

The first supplementary analysis tests if excluding *other* responses
(7.12% of total responses) affects the pattern of results.

```{r count-other}
sum(exp1_d$Other)
sum(exp1_d$Other) / length(exp1_d$Other)
```

Exclude *other* responses.

```{r subset-other}
exp1_d_noOther <- exp1_d %>% filter(Other == 0)
exp1_d_FF_noOther <- exp1_d_FF %>% filter(Other == 0)
```

## Model 1: Condition without *Other* Responses

Effect of Condition (first name, last name, full name) on likelihood of
a *she* response, as opposed to a *he* 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}
exp1_m_cond_noOther <- glmer(
  She ~ Condition + (1 | Participant) + (1 | Item),
  data = exp1_d_noOther, family = binomial
)
summary(exp1_m_cond_noOther)
```

No differences in results.

### Odds Ratios: Intercept

```{r OR-condiiton-other}
exp(get_intercept(exp1_m_cond_noOther))
exp(-get_intercept(exp1_m_cond_noOther))
```

0.32x less likely to use to use *she* overall (or: 3.10x more likely to
use *he* overall), p\<.001

### Odds Ratios: Last vs First+Full

```{r OR-LFF-other}
exp1_m_cond_noOther %>%
  tidy() %>%
  filter(term == "Conditionlast vs first/full") %>%
  pull(estimate) %>%
  exp()
```

19.89x more likely to use *she* in First + Full compared to Last (or:
19.89x 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}
exp1_d_noOther %<>% mutate(Condition_Last = case_when(
  Condition == "first" ~ 1,
  Condition == "full"  ~ 1,
  Condition == "last"  ~ 0
))
exp1_d_noOther$Condition_Last %<>% as.factor()
```

```{r model-L-other}
exp1_m_L_noOther <- glmer(
  She ~ Condition_Last + (1 | Participant) + (1 | Item),
  data = exp1_d_noOther, family = binomial
)
summary(exp1_m_L_noOther)
```

```{r OR-L-other}
exp(get_intercept(exp1_m_L_noOther))
exp(-get_intercept(exp1_m_L_noOther))
```

0.04x times less likely to use *she* in the Last Name condition (or:
22.29x more likely to use *he* 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}
exp1_d_noOther %<>% mutate(Condition_FF = case_when(
  Condition == "first" ~ 0,
  Condition == "full"  ~ 0,
  Condition == "last"  ~ 1
))
exp1_d_noOther$Condition_FF %<>% as.factor()
```

```{r model-FF-other}
exp1_m_FF_noOther <- glmer(
  She ~ Condition_FF + (1 | Participant) + (1 | Item),
  data = exp1_d_noOther, family = binomial
)
summary(exp1_m_FF_noOther)
```

```{r OR-FF-other}
exp(get_intercept(exp1_m_FF_noOther))
exp(-get_intercept(exp1_m_FF_noOther))
```

0.99x times less likely to use *she* in the First and Full Name
conditions (or: 1.01x more likely to use *he* in the n the First and
Full Name conditions) p=0.97

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

Effects of Condition (first name, full name) and the first name's Gender
Rating (centered, positive=more feminine) on the likelihood of a *she*
response as opposed to a *he* response, with *other* responses excluded.
In Experiment 1, 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}
exp1_m_nameGender_noOther <- glmer(
  She ~ Condition * GenderRatingCentered + (1 | Participant) + (1 | Item),
  data = exp1_d_FF_noOther, family = binomial
)
summary(exp1_m_nameGender_noOther)
```

Compared to the main analysis including *other* responses, the intercept
is trending instead of significant, the gender rating effect the same,
and the small First vs Full effect is no longer significant.

# 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}
exp1_d_FF %<>% mutate(GenderRatingSquared = GenderRatingCentered^2)
```

## Model 3: Quadratic

No quadratic effects.

```{r model-quad}
exp1_m_nameGender_quad <- glmer(
  She ~ Condition * GenderRatingCentered + Condition * GenderRatingSquared +
    (1 | Participant) + (1 | Item),
  data = exp1_d_FF, family = binomial
)
summary(exp1_m_nameGender_quad)
```

# 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}
exp1_d %>%
  group_by(SubjGenderMale) %>%
  summarise(total = n_distinct(Participant)) %>%
  kable()
```

For this analysis, we exclude participants who did not respond (N=15).
Because there are not enough participants to create 3 groups, we compare
male to non-male participants. Male participants (N=244) coded as 1 and
female (N=196), genderfluid (N=1), and nonbinary participants (N=1)
coded as 0.

```{r count-subjGender-coded}
exp1_d_subjGender <- exp1_d %>% filter(!is.na(SubjGenderMale))

exp1_d_subjGender %>%
  group_by(SubjGenderMale) %>%
  summarise(total = n_distinct(Participant)) %>%
  kable()
```

Summary of responses by condition and participant gender.

```{r means-subj-gender}
exp1_d_subjGender %<>% mutate(ResponseAll = case_when(
  He    == 1 ~ "He",
  She   == 1 ~ "She",
  Other == 1 ~ "Other"
))

exp1_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(
    She_HeOther = She / (He + Other),
    She_He = She / He
  ) %>%
  kable(digits = 3)
```

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

```{r contrast-coding-subj-gender}
exp1_d_subjGender$SubjGenderMale %<>% as.factor()
contrasts(exp1_d_subjGender$SubjGenderMale) <- cbind("NM_M" = c(-.5, .5))
contrasts(exp1_d_subjGender$SubjGenderMale)
```

Subset First and Full conditions.

```{r subset-FF-subj-gender}
exp1_d_FF_subjGender <- exp1_d_subjGender %>% filter(Condition != "last")
exp1_d_FF_subjGender$Condition %<>% droplevels()

contrasts(exp1_d_FF_subjGender$Condition) <-
  cbind("first vs full" = c(-.5, .5)) # add contrast back
contrasts(exp1_d_FF_subjGender$Condition)
```

## Model 4: Condition \* Participant Gender

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

```{r model-condition-subj-gender}
exp1_m_cond_subjGender <- glmer(
  She ~ Condition * SubjGenderMale + (1 | Participant) + (1 | Item),
  data = exp1_d_subjGender, family = binomial
)
summary(exp1_m_cond_subjGender)
```

Male participants are less likely to respond *she* overall than non-male
participants, but this is not significant after correcting for multiple
comparisons. Neither interaction with Condition is significant.

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

Effects of 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
a *he* or *other* responses. In Experiment 1, the Last Name condition
does not include any instances of the gendered first name, so it is not
included here. The model with random intercepts does not converge with
glmer, but does when using buildmer to find the maximal model (?).

```{r model-gender-rating-subj-gender}
exp1_m_nameGender_subjGender <- buildmer(
  formula = She ~ Condition * GenderRatingCentered * SubjGenderMale +
    (1 | Participant) + (1 | Item),
  data = exp1_d_FF_subjGender, family = binomial,
  buildmerControl(direction = c("order"), quiet = TRUE)
)
summary(exp1_m_nameGender_subjGender)
```

-   Participant Gender: n.s.

-   Condition (First vs Full) \* Participant Gender: There is a larger
    difference between the First and Full Name conditions for male
    participants (see means above), but this is n.s. after correcting
    for multiple comparisons.

-   Name Gender \* Participant Gender: There is a stronger effect of the
    first name gender rating for male participants, but this is n.s.
    after correction for multiple comparisons.

-   Condition (First vs Full) \* Name Gender \* Participant Gender:
    trending

# 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(exp1_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}
exp1_d_FF %<>% mutate(GenderRating4 = GenderRating - 4)
```

## Model 6: Gender Rating Recentered

```{r model-gender-rating-recenter}
exp1_m_recenter <- glmer(
  She ~ Condition * GenderRating4 + (1 | Participant) + (1 | Item),
  data = exp1_d_FF, family = binomial
)
summary(exp1_m_recenter)
```

Here, the beta estimate for the intercept has a larger absolute value
(-0.84 vs -0.51), and the beta estimate for the condition effect is
slightly higher (0.57 vs 0.53).