rethink_ANOVA_figure.Rmd

---
title             : "Figure 1 used in rethink ANOVA"
shorttitle         : "Figure 1 in Rethink ANOVA"

author: 
  - name: "Haiyang Jin"
    affiliation: ""
    address: "New York University Abu Dhabi, Saadiyat Isalnd, Abu Dhabi, United Arab Emirates"
    email: "haiyang.jin@outlook.com"
    corresponding: yes
    
affiliation:
  - id            : ""
    institution   : "New York University Abu Dhabi"
  
authornote        : |
  This is the code for creating the Figure 1 in the rethinking ANOVA paper.
        
date: "`r format(Sys.time(), '%d-%m-%Y')`"

---

```{r setup and load the related libraries, appendix, include=FALSE}
## load libraries
library(knitr)
library(tidyverse)
library(afex)
library(emmeans)
library(lme4)
library(lmerTest)
library(ggpubr)
library(here)
library(papaja)

theme_set(theme_apa())

# set global chunk options, put figures into folder
options(warn=-1, replace.assign=TRUE)
knitr::opts_chunk$set(
	echo = FALSE,
	include = TRUE,
	# warning = FALSE,
	fig.align = "center",
	fig.path = "figures/figure-",
	fig.show = "hold",
	fig.width=7, fig.asp =0.618,
	width = 1800, 
	message = FALSE
)

devtools::source_url("https://github.com/HaiyangJin/Website-Shared-Code/blob/master/simulate_data_lmm.R?raw=TRUE")
source(here("R", "funcs.R"))

```

# Interaction and simple effect analysis

## Sig interaction with sig simple effect
```{r}

params_ss <- list(
  # set the parameters for experiment design
  IV1_levels = c("aligned", "misaligned"),  # (has to be two levels)
  IV2_levels = c("incongruent", "congruent"),  # (has to be two levels)
  num_Subj = 30,
  num_Stim = 30,
  
  # set the mu for every bin (every condition)
  IV1.1_IV2.1 = 3,
  IV1.2_IV2.1 = 3.4,
  IV1.1_IV2.2 = 3.4,
  IV1.2_IV2.2 = 3.25,
  
  # set the variances for lmm (std)
  var_residual = .3,  # residual
  var_rnd_int_subj = .4,  # random intercept for Subject
  var_rnd_int_stim = .5,  # random intercept for Stimuli
  var_rnd_slp_IV1_subj = .6,  # random slope of IV1 for Subject
  var_rnd_slp_IV2_subj = .7,  # random slope of IV2 for Subject
  var_rnd_slp_inter_subj = .2,  # random slope of IV1*IV2 for Subject
  var_rnd_slp_IV1_stim = .8,  # random slope of IV1 for Stimuli
  var_rnd_slp_IV2_stim = .9,  # random slope of IV2 for Stimuli
  var_rnd_slp_inter_stim = .2  # random slope of IV1*IV2 for Stimuli
)

set.seed(2021)
df_simu_ss <- simudata_lmm(params = params_ss)
str(df_simu_ss)
```

```{r}
aov_simu_ss <- aov_4(Resp ~ IV1 * IV2 + (IV1 * IV2 | Subject),
                   fun_aggregate = mean,
                   data = df_simu_ss)
aov_simu_ss
```

```{r}
emm_simu_ss <- emmeans(aov_simu_ss, ~ IV1 + IV2)
(contr_simu_ss <- contrast(emm_simu_ss, "pairwise", adjust="none"))[c(1,2,5,6)]
```

```{r}
emmip(emm_simu_ss, IV2 ~ IV1, CIs = T)
```

## Sig interaction with non-sig simple effect
Significant interaction with non-significant simple effect analysis results:

```{r}
params_sn <- list(
  # set the parameters for experiment design
  IV1_levels = c("aligned", "misaligned"),  # (has to be two levels)
  IV2_levels = c("incongruent", "congruent"),  # (has to be two levels)
  num_Subj = 30,
  num_Stim = 30,

  # set the mu for every bin (every condition)
  IV1.1_IV2.1 = 3.20,
  IV1.2_IV2.1 = 3.00,
  IV1.1_IV2.2 = 2.85,
  IV1.2_IV2.2 = 2.90,

  # set the variances for lmm (std)
  var_residual = 1.00,  # residual
  var_rnd_int_subj = 1.00,  # random intercept for Subject
  var_rnd_int_stim = 1.00,  # random intercept for Stimuli
  var_rnd_slp_IV1_subj = 1.00,  # random slope of IV1 for Subject
  var_rnd_slp_IV2_subj = 1.00,  # random slope of IV2 for Subject
  var_rnd_slp_inter_subj = .20,  # random slope of IV1*IV2 for Subject
  var_rnd_slp_IV1_stim = 1.00,  # random slope of IV1 for Stimuli
  var_rnd_slp_IV2_stim = 1.00,  # random slope of IV2 for Stimuli
  var_rnd_slp_inter_stim = .20  # random slope of IV1*IV2 for Stimuli
)

set.seed(2021)
df_simu_sn <- simudata_lmm(params = params_sn)
str(df_simu_sn)
```

```{r}
aov_simu_sn <- aov_4(Resp ~ IV1 * IV2 + (IV1 * IV2 | Subject),
                   fun_aggregate = mean,
                   data = df_simu_sn)
aov_simu_sn
```

```{r}
emm_simu_sn <- emmeans(aov_simu_sn, ~ IV1 + IV2)
(contr_simu_sn <- contrast(emm_simu_sn, "pairwise", adjust="none"))[c(1,2,5,6)]
```

```{r}
emmip(emm_simu_sn, IV2 ~ IV1, CIs = T)
```

## Non-sig interaction with sig simple effect
Non-significant interaction with significant simple effect analysis results:
```{r}
params_ns <- list(
  # set the parameters for experiment design
  IV1_levels = c("aligned", "misaligned"),  # (has to be two levels)
  IV2_levels = c("congruent", "incongruent"),  # (has to be two levels)
  num_Subj = 30,
  num_Stim = 30,

  # set the mu for every bin (every condition)
  IV1.1_IV2.1 = 3.40,
  IV1.2_IV2.1 = 3.30,
  IV1.1_IV2.2 = 2.90,
  IV1.2_IV2.2 = 2.60,

  # set the variances for lmm (std)
  var_residual = .40,  # residual
  var_rnd_int_subj = .50,  # random intercept for Subject
  var_rnd_int_stim = .50,  # random intercept for Stimuli
  var_rnd_slp_IV1_subj = .50,  # random slope of IV1 for Subject
  var_rnd_slp_IV2_subj = .50,  # random slope of IV2 for Subject
  var_rnd_slp_inter_subj = .20,  # random slope of IV1*IV2 for Subject
  var_rnd_slp_IV1_stim = 1.00,  # random slope of IV1 for Stimuli
  var_rnd_slp_IV2_stim = 1.00,  # random slope of IV2 for Stimuli
  var_rnd_slp_inter_stim = .20  # random slope of IV1*IV2 for Stimuli
)

set.seed(2021)
df_simu_ns <- simudata_lmm(params = params_ns)
str(df_simu_ns)
```

```{r}
aov_simu_ns <- aov_4(Resp ~ IV1 * IV2 + (IV1 * IV2 | Subject),
                   fun_aggregate = mean,
                   data = df_simu_ns)
aov_simu_ns
```

```{r}
emm_simu_ns<- emmeans(aov_simu_ns, ~ IV1 + IV2)
(contr_simu_ns <- contrast(emm_simu_ns, "pairwise", adjust="none"))[c(1,2,5,6)]
```

```{r}
emmip(emm_simu_ns, IV2 ~ IV1, CIs = T)
```

## Non-sig interaction with non-sig simple effect
Non-significant interaction with non-significant simple effect analysis results:
```{r}
params_nn <- list(
  # set the parameters for experiment design
  IV1_levels = c("aligned", "misaligned"),  # (has to be two levels)
  IV2_levels = c("incongruent", "congruent"),  # (has to be two levels)
  num_Subj = 30,
  num_Stim = 30,

  # set the mu for every bin (every condition)
  IV1.1_IV2.1 = 3.20,
  IV1.2_IV2.1 = 3.20,
  IV1.1_IV2.2 = 3.00,
  IV1.2_IV2.2 = 2.90,

  # set the variances for lmm (std)
  var_residual = .40,  # residual
  var_rnd_int_subj = .50,  # random intercept for Subject
  var_rnd_int_stim = .50,  # random intercept for Stimuli
  var_rnd_slp_IV1_subj = .50,  # random slope of IV1 for Subject
  var_rnd_slp_IV2_subj = .50,  # random slope of IV2 for Subject
  var_rnd_slp_inter_subj = .20,  # random slope of IV1*IV2 for Subject
  var_rnd_slp_IV1_stim = 1.00,  # random slope of IV1 for Stimuli
  var_rnd_slp_IV2_stim = 1.00,  # random slope of IV2 for Stimuli
  var_rnd_slp_inter_stim = .20  # random slope of IV1*IV2 for Stimuli
)

set.seed(2021)
df_simu_nn <- simudata_lmm(params = params_nn)
str(df_simu_nn)
```

```{r}
aov_simu_nn <- aov_4(Resp ~ IV1 * IV2 + (IV1 * IV2 | Subject),
                   fun_aggregate = mean,
                   data = df_simu_nn)
aov_simu_nn
```

```{r}
emm_simu_nn<- emmeans(aov_simu_nn, ~ IV1 + IV2)
(contr_simu_nn <- contrast(emm_simu_nn, "pairwise", adjust="none"))[c(1,2,5,6)]
```

```{r}
emmip(emm_simu_nn, IV2 ~ IV1, CIs = T)
```

## Combined plots

```{r}

df_inter <- rbind(
  mutate(as_tibble(aov_simu_ss$anova_table)[3,],
         interaction = "significant", `simple effect` = "significant",
         x = 1.5, y = 3),
  mutate(as_tibble(aov_simu_sn$anova_table)[3,],
         interaction = "significant", `simple effect` = "nonsignificant",
         x = 1.5, y = 3),
  mutate(as_tibble(aov_simu_ns$anova_table)[3,],
         interaction = "nonsignificant", `simple effect` = "significant",
         x = 1.5, y = 3),
  mutate(as_tibble(aov_simu_nn$anova_table)[3,],
         interaction = "nonsignificant", `simple effect` = "nonsignificant",
         x = 1.5, y = 3)
) %>% 
  mutate(IV1 = "upright", IV2 = "intact",
         ptext = if_else(`Pr(>F)` < .001, paste0("italic(p)[inter] < .001"), 
                         paste0("italic(p)[inter] == ", round(`Pr(>F)`,3))),
         interaction = fct_relevel(interaction, "significant", "nonsignificant"),
         `simple effect` = fct_relevel(`simple effect`, "significant", "nonsignificant"))

df_simp <- rbind(
  mutate(filter(as_tibble(contr_simu_ss)[c(1,2,5,6)], p.value==min(p.value)),
         interaction = "significant", `simple effect` = "significant",
         x = 1.5, y = 2.85),
  mutate(filter(as_tibble(contr_simu_sn)[c(1,2,5,6)], p.value==min(p.value)),
         interaction = "significant", `simple effect` = "nonsignificant",
         x = 1.5, y = 2.85),
  mutate(filter(as_tibble(contr_simu_ns)[c(1,2,5,6)], p.value==min(p.value)),
         interaction = "nonsignificant", `simple effect` = "significant",
         x = 1.5, y = 2.85),
  mutate(filter(as_tibble(contr_simu_nn)[c(1,2,5,6)], p.value==min(p.value)),
         interaction = "nonsignificant", `simple effect` = "nonsignificant",
         x = 1.5, y = 2.85)
) %>% 
  mutate(IV1 = "upright", IV2 = "intact",
         labeltext_inter = paste0(interaction, "~interaction"),
         labeltext_sim = paste0(`simple effect`, "~simple~effects"),
         ptext = if_else(`p.value` < .001, paste0("italic(p)[min_sim] < .001"), 
                         paste0("italic(p)[min_sim] == ", round(`p.value`,3))),
         interaction = fct_relevel(interaction, "significant", "nonsignificant"),
         `simple effect` = fct_relevel(`simple effect`, "significant", "nonsignificant"))

```

```{r fig.asp=.7, fig.width=3}
theme_set(theme_apa())

rbind(mutate(as_tibble(emm_simu_ss),
             interaction = "significant", `simple effect` = "significant"),
      mutate(as_tibble(emm_simu_sn),
             interaction = "significant", `simple effect` = "nonsignificant"),
      mutate(as_tibble(emm_simu_ns),
             interaction = "nonsignificant", `simple effect` = "significant"),
      mutate(as_tibble(emm_simu_nn),
             interaction = "nonsignificant", `simple effect` = "nonsignificant")
) %>% 
  mutate(IV2 = fct_relevel(IV2, "congruent", "incongruent"),
         interaction = fct_relevel(interaction, "significant", "nonsignificant"),
         `simple effect` = fct_relevel(`simple effect`, "significant", "nonsignificant")) %>% 
  ggplot(aes(IV1, emmean, group=IV2, color=IV2)) +
  geom_point(size = 2, position=position_dodge(.1)) +
  geom_line(aes(linetype=IV2), size = 1, position=position_dodge(.1)) +
  geom_errorbar(aes(ymin=lower.CL, ymax=upper.CL), width=0.15, 
                position=position_dodge(.1), show.legend=F) +
  facet_grid(`simple effect` ~ interaction, labeller = label_both) +
  geom_text(aes(label=ptext, x=x, y=y), data=df_inter,
            color="black", size = 3, show.legend = F, parse=T) +
  geom_text(aes(label=ptext, x=x, y=y), data=df_simp,
            color="black", size = 3, show.legend = F, parse=T) +
  labs(x="Alignment", y=expression("Sensitivity"~italic("d'")), 
       color="Congruency", linetype="Congruency") +
  theme(legend.position=c(.5, .5)) +
  NULL

# ggsave(file="inter_simple_sig.png", width = 7.2, height = 5.4)
```

```{r fig.asp=.7, fig.width=3}
theme_set(theme_apa())

rbind(mutate(as_tibble(emm_simu_ss),
             interaction = "significant", `simple effect` = "significant"),
      mutate(as_tibble(emm_simu_sn),
             interaction = "significant", `simple effect` = "nonsignificant"),
      mutate(as_tibble(emm_simu_ns),
             interaction = "nonsignificant", `simple effect` = "significant"),
      mutate(as_tibble(emm_simu_nn),
             interaction = "nonsignificant", `simple effect` = "nonsignificant")
) %>% 
  mutate(IV2 = fct_relevel(IV2, "congruent", "incongruent"),
         interaction = fct_relevel(interaction, "significant", "nonsignificant"),
         `simple effect` = fct_relevel(`simple effect`, "significant", "nonsignificant")) %>% 
  ggplot(aes(IV1, emmean, group=IV2, color=IV2)) +
  geom_point(size = 2, position=position_dodge(.1)) +
  geom_line(aes(linetype=IV2), size = 1, position=position_dodge(.1)) +
  geom_errorbar(aes(ymin=lower.CL, ymax=upper.CL), width=0.15, 
                position=position_dodge(.1), show.legend=F) +
  facet_grid(`simple effect` ~ interaction) +
  geom_text(aes(label=labeltext_inter), data=df_simp, x=.5, y = 4.5,
            color="black", size = 3, hjust=0, show.legend = F, parse=T) +
  geom_text(aes(label=labeltext_sim), data=df_simp, x=.5, y = 4.3,
            color="black", size = 3, hjust=0, show.legend = F, parse=T) +
  geom_text(aes(label=ptext, x=x, y=y), data=df_inter,
            color="black", size = 3, show.legend = F, parse=T) +
  geom_text(aes(label=ptext, x=x, y=y), data=df_simp,
            color="black", size = 3, show.legend = F, parse=T) +
  labs(x="Alignment", y=expression("Sensitivity"~italic("d'")),
       color="Congruency", linetype="Congruency") +
  ylim(c(2.25, 4.45)) +
  # theme_apa_nostrip() +
  # theme(legend.position="bottom") +
  theme(legend.position=c(.5,.55), legend.direction="horizontal") +
  NULL

# ggsave(file=here::here("images", "inter_simple_sig.png", width = 7.2, height = 5.4)
```