Add tp3 bis

M1/General Linear Models/TP3-bis/TP3.Rmd

@@ -0,0 +1,206 @@
+```{r}
+setwd('/Users/arthurdanjou/Workspace/studies/M1/General Linear Models/TP3-bis')
+
+library(GGally)
+library(broom)
+library(scales)
+library(car)
+library(glue)
+library(janitor)
+library(marginaleffects)
+library(tidyverse)
+library(qqplotr)
+options(scipen = 999, digits = 5)
+```
+```{r}
+data03 <- read.csv('data03.csv', header = TRUE, sep = ',', dec = '.')
+data03$sexe <- as.factor(data03$sexe)
+data03$travail <- as.factor(data03$travail)
+head(data03, 15)
+```
+```{r}
+tab_sexe <- data03 |>
+  count(sexe) |>
+  mutate(freq1 = n / sum(n)) |>
+  mutate(freq2 = glue("{n} ({label_percent()(freq1)})")) |>
+  rename(Sexe = 1, Effectif = n, Proportion = freq1, "n (%)" = freq2)
+tab_sexe
+```
+
+```{r}
+tab_travail <- data03 |>
+  count(travail) |>
+  mutate(freq1 = n / sum(n)) |>
+  mutate(freq2 = glue("{n} ({label_percent()(freq1)})")) |>
+  rename(Travail = 1, Effectif = n, Proportion = freq1, "n (%)" = freq2)
+tab_travail
+```
+
+```{r}
+cross_sexe_travail <- data03 |>
+  count(sexe, Travail = travail) |>
+  group_by(sexe) |>
+  mutate(freq1 = n / sum(n)) |>
+  mutate(freq2 = glue("{n} ({label_percent(0.1)(freq1)})"), n = NULL, freq1 = NULL) |>
+  pivot_wider(names_from = sexe, values_from = freq2)
+cross_sexe_travail
+```
+
+```{r}
+data03 <- mutate(data03, logy = log(y))
+
+data03 |>
+  pivot_longer(c(y, logy), names_to = "variable", values_to = "value") |>
+  mutate(variable = factor(
+    variable,
+    levels = c("y", "logy"),
+    labels = c("Salaire", "Log-Salaire"))
+  ) |>
+  ggplot(aes(x = value)) +
+  facet_wrap(vars(variable), scales = "free") +
+  geom_histogram(
+    fill = "dodgerblue",
+    color = "black",
+    bins = 15) +
+  scale_y_continuous(expand = expansion(c(0, 0.05))) +
+  scale_x_continuous(breaks = pretty_breaks()) +
+  labs(x = "Valeur", y = "Effectif") +
+  theme_bw(base_size = 14) +
+  theme(strip.text = element_text(size = 11, face = "bold"))
+```
+```{r}
+data03 |>
+  pivot_longer(c(y, logy), names_to = "variable", values_to = "value") |>
+  mutate(variable = factor(
+    variable,
+    levels = c("y", "logy"), labels = c("Salaire", "Log-Salaire")
+  )) |>
+  ggplot(aes(x = sexe, y = value)) +
+  facet_wrap(vars(variable), scales = "free") +
+  geom_boxplot(
+    width = 0.5, fill = "cyan", linewidth = 0.5, outlier.size = 2, outlier.alpha = 0.3
+  ) +
+  scale_y_continuous(breaks = pretty_breaks()) +
+  labs(x = NULL, y = "Valeur") +
+  theme_bw(base_size = 14) +
+  theme(
+    strip.text = element_text(size = 11, face = "bold"),
+    panel.border = element_rect(linewidth = 0.5)
+  )
+```
+```{r}
+data03 |>
+  pivot_longer(c(y, logy), names_to = "variable", values_to = "value") |>
+  mutate(variable = factor(
+    variable,
+    levels = c("y", "logy"), labels = c("Salaire", "Log-Salaire")
+  )) |>
+  ggplot(aes(x = travail, y = value)) +
+  facet_wrap(vars(variable), scales = "free") +
+  stat_boxplot(width = 0.25, geom = "errorbar", linewidth = 0.5) +
+  geom_boxplot(
+    width = 0.5, fatten = 0.25, fill = "cyan", linewidth = 0.5,
+    outlier.size = 2, outlier.alpha = 0.3
+  ) +
+  scale_y_continuous(breaks = pretty_breaks()) +
+  labs(x = NULL, y = "Valeur") +
+  theme_bw(base_size = 14) +
+  theme(
+    strip.text = element_text(size = 11, face = "bold"),
+    panel.border = element_rect(linewidth = 0.5)
+  )
+```
+
+```{r}
+data03 |>
+  group_by(sexe) |>
+  summarise(n = n(), "Mean (Salaire)" = mean(y), "SD (Salaire)" = sd(y))
+```
+
+```{r}
+data03 |>
+  group_by(travail) |>
+  summarise(n = n(), "Mean (Salaire)" = mean(y), "SD (Salaire)" = sd(y))
+```
+
+```{r}
+data03 |>
+  group_by(sexe, travail) |>
+  summarise(n = n(), "Mean (Salaire)" = mean(y), "SD (Salaire)" = sd(y))
+```
+```{r}
+data03 |>
+  group_by(sexe) |>
+  summarise(n = n(), "Mean (Salaire)" = mean(logy), "SD (Salaire)" = sd(logy))
+```
+
+```{r}
+data03 |>
+  group_by(travail) |>
+  summarise(n = n(), "Mean (Salaire)" = mean(logy), "SD (Salaire)" = sd(logy))
+```
+
+```{r}
+data03 |>
+  group_by(sexe, travail) |>
+  summarise(n = n(), "Mean (Salaire)" = mean(logy), "SD (Salaire)" = sd(logy))
+```
+```{r}
+data03 <- data03 |>
+  mutate(sexef = ifelse(sexe == "Femme", 1, 0), sexeh = 1 - sexef) |>
+  mutate(job1 = (travail == "Type 1") * 1) |>
+  mutate(job2 = (travail == "Type 2") * 1) |>
+  mutate(job3 = (travail == "Type 3") * 1)
+head(data03, 15)
+```
+```{r}
+mod1 <- lm(y ~ sexeh, data = data03)
+mod2 <- lm(y ~ job2 + job3, data = data03)
+mod3 <- lm(y ~ sexeh + job2 + job3, data = data03)
+tidy(mod1)
+tidy(mod2)
+tidy(mod3)
+```
+
+Interprétations des coefficients du modèle 1
+$𝑦_i = β_0 + β_1 sexeh_i + ϵ_i$
+• (Intercept): $\hat{β_0} = 7.88$ : Salaire moyen chez les femmes
+• sexeh: $\hat{𝛽1} = 2.12$ : Les hommes gagnent en moyenne 2.12 dollars par heure de plus que les femmes
+(significatif).
+
+Interprétations des coefficients du modèle 2
+$𝑦_i = β_0 + β_1 job2_i + β_2 job3_i + ϵ_i$
+• (Intercept): $\hat{β_0} = 12.21$ : Salaire moyen pour le travail de type 1.
+• job2: $\hat{β_1} = −5.09$ : la différence de salaire entre le travail de type 2 et celui de type 1 est de −5.09 dollars par heure en moyenne (significatif)
+• job3: $\hat{β_2} = −3.78$ : la différence de salaire entre le travail de type 3 et celui de type 1 est de −3.78 dollarspar heure en moyenne (significatif).
+
+Interprétations des coefficients du modèle 3
+$𝑦_i = β_0 + β_1 sexeh_i + β_2 job2_i + β_3 job3_i + ϵ_i$
+• (Intercept): $\hat{β_0} = 11.13$ : Salaire moyen chez les femmes avec un travail de type 1
+• sexeh: $\hat{β_1 = 1.97$ : Les hommes gagnent en moyenne 1.97 dollars par heure de plus que les femmes
+(significatif), quelque soit le type de travail.
+• job2: $\hat{β_2} = −4.71$ : la différence de salaire entre le travail de type 2 et celui de type 1 est de −4.71 dollars par heure en moyenne (significatif), quelque soit le sexe.
+• job3: $\hat{β_3} = −4.3$ : la différence de salaire entre le travail de type 3 et celui de type 1 est de −4.3 dollars par heure en moyenne (significatif), quelque soit le sexe.
+
+```{r}
+anova(mod1, mod3)
+```
+La p-value du test est inférieur à 0.05, on rejette donc $𝐻0$ et on conclue qu’au moins un des coefficients (𝛽1, 𝛽2) est significativement non nulle.
+• On vient de tester si le type de travail est associé au salaire horaire. C’est donc le cas pour ces données.
+```{r}
+linearHypothesis(mod3, c("job2", "job3"))
+linearHypothesis(mod3, "job2 = job3")
+```
+Le test est non significatif (𝑝 = 0.44). On ne rejette pas $𝐻0$ et on conclue qu’il n’y pas de différence de salaire horaire entre le travail de type 2 et le travail de type 3, quelque soit le sexe.
+```{r}
+mod3bis <- lm(y ~ sexe + travail, data = data03)
+summary(mod3bis)
+```
+Les modèles mod3bis1 et mod3 sont identiques
+• Pas besoins de créer toutes ces variables indicatrices si nos variables catégorielles sont de type factor !
+• La référence sera toujours la première modalité du factor.
+• On peut changer la référence avec `relevel()` ou avec `C()`. Par exemple, si on veut la modalité 2 en référence pour le travail
+```{r}
+lm(y ~ sexe + relevel(travail, ref = 2), data = data03) |>
+  tidy()
+```

M1/General Linear Models/TP3-bis/data03.csv

@@ -0,0 +1,535 @@
+id,y,education,experience,sexe,travail
+1,3.75,12,6,Femme,Type 3
+2,12,16,14,Femme,Type 1
+3,15.73,16,4,Homme,Type 1
+4,5,12,0,Femme,Type 2
+5,9,12,20,Homme,Type 2
+6,6.88,17,15,Femme,Type 1
+7,9.1,13,16,Homme,Type 2
+8,3.35,16,3,Homme,Type 2
+9,10,16,10,Femme,Type 1
+10,4.59,12,36,Femme,Type 2
+11,7.61,12,20,Homme,Type 3
+12,18.5,14,13,Femme,Type 3
+13,20.4,17,3,Homme,Type 1
+14,8.49,12,24,Femme,Type 2
+15,12.5,15,6,Femme,Type 2
+16,5.75,9,34,Femme,Type 1
+17,4,12,12,Homme,Type 2
+18,12.47,13,10,Homme,Type 3
+19,5.55,11,45,Femme,Type 2
+20,6.67,16,10,Femme,Type 1
+21,4.75,12,2,Femme,Type 2
+22,7,12,7,Homme,Type 3
+23,12.2,14,10,Homme,Type 3
+24,15,12,42,Homme,Type 1
+25,9.56,12,23,Homme,Type 3
+26,7.65,12,20,Homme,Type 2
+27,5.8,13,5,Homme,Type 2
+28,5.8,16,14,Homme,Type 1
+29,3.6,12,6,Femme,Type 2
+30,7.5,12,3,Homme,Type 3
+31,8.75,12,30,Homme,Type 1
+32,10.43,14,15,Femme,Type 2
+33,3.75,12,41,Femme,Type 2
+34,8.43,12,12,Homme,Type 2
+35,4.55,12,4,Femme,Type 1
+36,6.25,9,30,Homme,Type 3
+37,4.5,12,16,Homme,Type 3
+38,4.3,13,8,Homme,Type 3
+39,8,12,15,Femme,Type 2
+40,7,7,42,Homme,Type 3
+41,4.5,12,3,Femme,Type 1
+42,4.75,12,10,Femme,Type 2
+43,4.5,12,7,Femme,Type 1
+44,3.4,8,49,Femme,Type 2
+45,9.83,12,23,Homme,Type 3
+46,6.25,16,7,Femme,Type 1
+47,23.25,17,25,Femme,Type 1
+48,9,16,27,Femme,Type 2
+49,19.38,16,11,Femme,Type 1
+50,14,16,16,Femme,Type 1
+51,6.5,12,8,Homme,Type 3
+52,6,12,19,Femme,Type 2
+53,6.25,16,7,Femme,Type 1
+54,6.5,8,27,Homme,Type 3
+55,9.5,12,25,Femme,Type 2
+56,4.25,12,29,Femme,Type 2
+57,14.53,16,18,Homme,Type 1
+58,8.85,14,19,Femme,Type 2
+59,9.17,12,44,Femme,Type 2
+60,11,8,42,Homme,Type 3
+61,3.75,16,13,Femme,Type 3
+62,3.35,14,0,Homme,Type 2
+63,3.35,12,8,Femme,Type 3
+64,6.75,12,12,Homme,Type 3
+65,10,16,7,Femme,Type 2
+66,8.93,8,47,Homme,Type 2
+67,11.11,12,28,Homme,Type 2
+68,6.5,11,39,Homme,Type 2
+69,14,5,44,Homme,Type 3
+70,6.25,13,30,Femme,Type 2
+71,4.7,8,19,Homme,Type 3
+72,22.83,18,37,Femme,Type 1
+73,13.45,12,16,Homme,Type 3
+74,5,12,39,Femme,Type 2
+75,10,10,12,Homme,Type 3
+76,8.9,10,27,Homme,Type 3
+77,7,11,12,Femme,Type 2
+78,15,12,39,Homme,Type 1
+79,3.5,12,35,Homme,Type 2
+80,12.57,12,12,Homme,Type 3
+81,8,12,14,Femme,Type 2
+82,7,18,33,Homme,Type 1
+83,26,14,21,Homme,Type 3
+84,11.43,12,3,Homme,Type 3
+85,5.56,14,5,Homme,Type 2
+86,12,18,18,Femme,Type 1
+87,5,12,4,Homme,Type 2
+88,9.15,12,7,Homme,Type 3
+89,8.5,12,16,Femme,Type 1
+90,6.25,16,4,Homme,Type 2
+91,3.35,7,43,Homme,Type 3
+92,15.38,16,33,Homme,Type 1
+93,6.1,12,33,Femme,Type 1
+94,4.13,12,4,Femme,Type 2
+95,14.21,11,15,Homme,Type 3
+96,7.53,14,1,Homme,Type 2
+97,3.5,10,33,Femme,Type 2
+98,6.58,12,24,Femme,Type 1
+99,4.85,10,13,Homme,Type 3
+100,7.81,12,1,Femme,Type 1
+101,6,13,31,Homme,Type 2
+102,4.5,11,14,Homme,Type 3
+103,24.98,18,29,Homme,Type 1
+104,13.33,18,10,Homme,Type 2
+105,20.5,16,14,Homme,Type 1
+106,10,12,20,Homme,Type 2
+107,11.22,18,19,Homme,Type 1
+108,10.58,16,9,Homme,Type 1
+109,12.65,17,13,Femme,Type 1
+110,12,12,14,Homme,Type 3
+111,5.1,8,21,Femme,Type 3
+112,9.86,15,13,Homme,Type 1
+113,10,12,11,Homme,Type 3
+114,8,18,33,Homme,Type 1
+115,22.2,18,40,Femme,Type 1
+116,4.25,13,0,Femme,Type 2
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+119,12.5,13,16,Femme,Type 2
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+141,7.5,12,9,Femme,Type 2
+142,7.78,16,6,Femme,Type 1
+143,4.5,12,7,Femme,Type 3
+144,3.5,9,48,Homme,Type 2
+145,10.2,17,26,Femme,Type 1
+146,12,17,24,Femme,Type 1
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+148,6,17,3,Femme,Type 1
+149,13.51,18,14,Homme,Type 1
+150,7.5,16,10,Homme,Type 1
+151,12,12,20,Homme,Type 3
+152,4,11,25,Femme,Type 3
+153,12.5,12,43,Homme,Type 2
+154,15,12,33,Homme,Type 3
+155,10,18,13,Femme,Type 1
+156,3.65,11,16,Homme,Type 3
+157,7,11,16,Femme,Type 2
+158,8.9,14,13,Homme,Type 3
+159,25,14,4,Homme,Type 2
+160,7,12,32,Femme,Type 1
+161,14.29,14,32,Femme,Type 2
+162,4.22,8,39,Femme,Type 3
+163,7.3,12,37,Homme,Type 3
+164,13.65,16,11,Homme,Type 1
+165,7.5,12,16,Femme,Type 2
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+167,7.78,12,23,Homme,Type 3
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+170,10,16,0,Femme,Type 1
+171,17.25,15,31,Homme,Type 1
+172,12,17,13,Homme,Type 2
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+174,3.35,13,2,Femme,Type 2
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+184,4.55,13,33,Femme,Type 2
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+203,7.45,12,25,Femme,Type 1
+204,4.84,15,1,Homme,Type 1
+205,6,4,54,Homme,Type 2
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+218,8.99,12,15,Femme,Type 2
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+222,12.5,14,19,Femme,Type 2
+223,7,17,2,Homme,Type 1
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+225,19.98,14,44,Homme,Type 2
+226,6.5,10,30,Homme,Type 3
+227,9.5,12,39,Femme,Type 2
+228,11.25,12,41,Homme,Type 3
+229,8.06,13,17,Homme,Type 1
+230,6,15,26,Femme,Type 2
+231,24.98,17,18,Homme,Type 1
+232,5,12,28,Femme,Type 3
+233,3.98,14,6,Femme,Type 2
+234,4.5,13,0,Femme,Type 2
+235,7.75,12,24,Femme,Type 2
+236,2.85,12,1,Homme,Type 3
+237,9,16,7,Homme,Type 1
+238,9.63,14,22,Homme,Type 2
+239,12,14,10,Femme,Type 1
+240,7.5,12,27,Femme,Type 2
+241,13.45,16,16,Homme,Type 1
+242,7.5,12,23,Femme,Type 2
+243,4.5,7,14,Homme,Type 2
+244,3.75,12,17,Femme,Type 2
+245,5.75,12,3,Homme,Type 1
+246,12.5,17,13,Femme,Type 1
+247,6.5,12,11,Femme,Type 1
+248,6.94,12,7,Femme,Type 2
+249,11.36,18,5,Homme,Type 1
+250,3.35,12,0,Femme,Type 2
+251,9.22,14,13,Femme,Type 1
+252,9.75,15,9,Femme,Type 3
+253,24.98,17,5,Femme,Type 1
+254,5.62,13,2,Femme,Type 2
+255,9.57,12,5,Femme,Type 2
+256,5.5,12,11,Femme,Type 3
+257,7,12,10,Femme,Type 2
+258,17.86,13,36,Homme,Type 1
+259,5.5,16,2,Femme,Type 2
+260,8.8,14,41,Homme,Type 1
+261,5.35,12,13,Femme,Type 2
+262,4.95,9,42,Femme,Type 3
+263,13.89,16,17,Femme,Type 1
+264,6,12,1,Homme,Type 3
+265,4.17,14,24,Femme,Type 2
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