190824_学力差の検討_社会
今回の課題
- 学級規模に関係なく，どこで学力差が生じるのか
- (a)は学級規模で説明されるのか
- 学力の変動の大きさは，prior achievementで説明されるのか
- (a)に対する(b)と(c)の交互作用は見られるか
とりあえず社会をやってる
NRTデータを読み込む
setwd("/Users/koyo/Dropbox/000078_CSKAKEN/04_NRT/SY2018")
nrt.all <- read.csv("nrt.csv", fileEncoding = "Shift_JIS")
setwd("/Users/koyo/Dropbox/000078_CSKAKEN/190700_Anal")社会のデータに限定する
nrt.shak <- nrt.all %>%
dplyr::select(c("renban", "sho.sid",
"shak.ss.1415",
"shak.ss.1516",
"shak.ss.1617",
"shak.ss.1718" #6-7年生追加
))
colnames(nrt.shak) <- c("renban", "sid",
"g34.shak",
"g45.shak",
"g56.shak",
"g67.shak"
)
nrt.shak <- nrt.shak%>%
mutate(id = row_number())
# write.csv(nrt.shak, "nrt_shak.csv")全体について，学年間の分散比を求めてみる
library(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:brms':
##
## cs## The following objects are masked from 'package:ggplot2':
##
## %+%, alphag34.ds <- describe(nrt.shak$g34.shak)
g45.ds <- describe(nrt.shak$g45.shak)
g56.ds <- describe(nrt.shak$g56.shak)
g67.ds <- describe(nrt.shak$g67.shak)
#平均差と分散比
d45 <- matrix(c(g45.ds[,3] - g34.ds[,3], g45.ds[,4]^2 / g34.ds[,4]^2), nrow=1, ncol=2)
d56 <- matrix(c(g56.ds[,3] - g45.ds[,3], g56.ds[,4]^2 / g45.ds[,4]^2), nrow=1, ncol=2)
d67 <- matrix(c(g67.ds[,3] - g56.ds[,3], g67.ds[,4]^2 / g56.ds[,4]^2), nrow=1, ncol=2)
diff.1 <- rbind(d45, d56, d67)
colnames(diff.1) <- c("M.Diff", "V.Ratio")
rownames(diff.1) <- c("d45", "d56", "d67")
diff.1## M.Diff V.Ratio
## d45 -0.5099369 0.8925809
## d56 0.1868797 1.0660894
## d67 0.3005566 1.0490981変動係数(標準偏差/平均)を求めてみる
cv4 <- g34.ds[,4] / g34.ds[,3]
cv5 <- g45.ds[,4] / g45.ds[,3]
cv6 <- g56.ds[,4] / g56.ds[,3]
cv7 <- g67.ds[,4] / g67.ds[,3]
cv.1 <- matrix(c(cv4, cv5, cv6, cv7), nrow=4, ncol=1)
colnames(cv.1) <- c("cv")
rownames(cv.1) <- c("3-4","4-5","5-6","6-7")
cv.1## cv
## 3-4 0.2056346
## 4-5 0.1961718
## 5-6 0.2018289
## 6-7 0.2055464変動係数の学年間の比を求めてみる
cv.ratio45 <- cv.1[2]/ cv.1[1]
cv.ratio56 <- cv.1[3]/ cv.1[2]
cv.ratio67 <- cv.1[4]/ cv.1[3]
cv.ratio1 <- matrix(c(cv.ratio45, cv.ratio56, cv.ratio67), nrow=3, ncol=1)
colnames(cv.ratio1) <- c("cv.rario")
rownames(cv.ratio1) <- c("4-5","5-6", "6-7")
cv.ratio1## cv.rario
## 4-5 0.9539828
## 5-6 1.0288373
## 6-7 1.0184192学校ごとに変動係数を求める
g34.mean <- nrt.shak[c("sid", "g34.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(avg.34 = mean(g34.shak))
g34.sd <- nrt.shak[c("sid", "g34.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(sd.34 = sd(g34.shak))
g34.msd <-data.frame(dplyr::inner_join(g34.mean, g34.sd, by = "sid"))
g45.mean <- nrt.shak[c("sid", "g45.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(avg.45 = mean(g45.shak))
g45.sd <- nrt.shak[c("sid", "g45.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(sd.45 = sd(g45.shak))
g45.msd <-data.frame(dplyr::inner_join(g45.mean, g45.sd, by = "sid"))
g56.mean <- nrt.shak[c("sid", "g56.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(avg.56 = mean(g56.shak))
g56.sd <- nrt.shak[c("sid", "g56.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(sd.56 = sd(g56.shak))
g56.msd <-data.frame(dplyr::inner_join(g56.mean, g56.sd, by = "sid"))
g67.mean <- nrt.shak[c("sid", "g67.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(avg.67 = mean(g67.shak))
g67.sd <- nrt.shak[c("sid", "g67.shak")] %>% na.omit() %>% group_by(sid) %>% summarise(sd.67 = sd(g67.shak))
g67.msd <-data.frame(dplyr::inner_join(g67.mean, g67.sd, by = "sid"))
g345.msd <- data.frame(dplyr::full_join(g34.msd, g45.msd, by = "sid"))
g3456.msd <- data.frame(dplyr::full_join(g345.msd, g56.msd, by = "sid"))
g37.msd <- data.frame(dplyr::full_join(g3456.msd, g67.msd, by = "sid"))
g37.msd <- g37.msd %>% dplyr::mutate(cv34 = sd.34 / avg.34)
g37.msd <- g37.msd %>% dplyr::mutate(cv45 = sd.45 / avg.45)
g37.msd <- g37.msd %>% dplyr::mutate(cv56 = sd.56 / avg.56)
g37.msd <- g37.msd %>% dplyr::mutate(cv67 = sd.67 / avg.67)
g37.msd <- g37.msd %>% dplyr::mutate(cvr.45 = cv45 / cv34)
g37.msd <- g37.msd %>% dplyr::mutate(cvr.56 = cv56 / cv45)
g37.msd <- g37.msd %>% dplyr::mutate(cvr.67 = cv67 / cv56)
#head(g16.msd)
hist(g37.msd$cvr.45, breaks=seq(0,4,0.2), main="cvr.45", xlab="cvr", ylim=c(0,120), xlim=c(0,4))
hist(g37.msd$cvr.56, breaks=seq(0,4,0.2), main="cvr.56", xlab="cvr", ylim=c(0,120), xlim=c(0,4))
hist(g37.msd$cvr.67, breaks=seq(0,4,0.2), main="cvr.56", xlab="cvr", ylim=c(0,120), xlim=c(0,4))
## 学級規模データの読み込み
setwd("/Users/koyo/Dropbox/000078_CSKAKEN/01_CSNC")
csnc.all <- read_excel("sho_csnc.xlsx")
# 学校データ整形
setwd("/Users/koyo/Dropbox/000078_CSKAKEN/190700_Anal")
#### 統廃合のない学校のみを対象 複式設置校を除外
csnc.taisho_ <- dplyr::filter(csnc.all, taisho.g1 == 1 &
togo == 0 & nonrt == 0 & fuku == 0)
# 学校データを数値型にする
csnc.taisho <- select(csnc.taisho_,(c("taisho", "sid.new",
"nc.g1", "csmean.g1",
"nc.g2", "csmean.g2",
"nc.g3", "csmean.g3",
"nc.g4", "csmean.g4",
"nc.g5", "csmean.g5",
"nc.g6", "csmean.g6"
)))
csnc.taisho$taisho <- as.numeric(csnc.taisho$taisho)
csnc.taisho$sid.new <- as.numeric(csnc.taisho$sid.new)
csnc.taisho$nc.g1 <- as.numeric(csnc.taisho$nc.g1)
csnc.taisho$csmean.g1 <- as.numeric(csnc.taisho$csmean.g1)
csnc.taisho$nc.g2 <- as.numeric(csnc.taisho$nc.g2)
csnc.taisho$csmean.g2 <- as.numeric(csnc.taisho$csmean.g2)
csnc.taisho$nc.g3 <- as.numeric(csnc.taisho$nc.g3)
csnc.taisho$csmean.g3 <- as.numeric(csnc.taisho$csmean.g3)
csnc.taisho$nc.g4 <- as.numeric(csnc.taisho$nc.g4)
csnc.taisho$csmean.g4 <- as.numeric(csnc.taisho$csmean.g4)
csnc.taisho$nc.g5 <- as.numeric(csnc.taisho$nc.g5)
csnc.taisho$csmean.g5 <- as.numeric(csnc.taisho$csmean.g5)
csnc.taisho$nc.g6 <- as.numeric(csnc.taisho$nc.g6)
csnc.taisho$csmean.g6 <- as.numeric(csnc.taisho$csmean.g6)
csnc.nona <- na.omit(csnc.taisho)
colnames(csnc.nona) <- c("taisho", "sid",
"nc.g1", "cs.g1",
"nc.g2", "cs.g2",
"nc.g3", "cs.g3",
"nc.g4", "cs.g4",
"nc.g5", "cs.g5",
"nc.g6", "cs.g6"
)
csnc <- csnc.nona[,2:14]
## 学級規模を中心化する
### 各学年での平均
cs.m.g1 <- mean(csnc$cs.g1)
cs.m.g2 <- mean(csnc$cs.g2)
cs.m.g3 <- mean(csnc$cs.g3)
cs.m.g4 <- mean(csnc$cs.g4)
cs.m.g5 <- mean(csnc$cs.g5)
cs.m.g6 <- mean(csnc$cs.g6)
### 各学年の平均の平均
csm <- matrix(c(cs.m.g1, cs.m.g2, cs.m.g3, cs.m.g4, cs.m.g5, cs.m.g6), nrow=6, ncol=1)
csnc$cs.c.g1 <- csnc$cs.g1 - mean(csm)
csnc$cs.c.g2 <- csnc$cs.g2 - mean(csm)
csnc$cs.c.g3 <- csnc$cs.g3 - mean(csm)
csnc$cs.c.g4 <- csnc$cs.g4 - mean(csm)
csnc$cs.c.g5 <- csnc$cs.g5 - mean(csm)
csnc$cs.c.g6 <- csnc$cs.g6 - mean(csm)
## 学級規模変動差分データ列作成
csnc$cs.d12 <- csnc$cs.g2 - csnc$cs.g1
csnc$cs.d23 <- csnc$cs.g3 - csnc$cs.g2
csnc$cs.d34 <- csnc$cs.g4 - csnc$cs.g3
csnc$cs.d45 <- csnc$cs.g5 - csnc$cs.g4
csnc$cs.d56 <- csnc$cs.g6 - csnc$cs.g5 学級規模データと学校ごとの変動係数データを結合する
# 4-5年生
cs.45 <- csnc[c("sid", "nc.g4", "cs.g4", "cs.c.g4", "cs.d34")]
cvr.45 <- g37.msd[c("sid", "avg.34", "avg.45", "cvr.45")]
cs.cvr.45<-na.omit(data.frame(dplyr::inner_join(cs.45, cvr.45, by = "sid")))
# 5-6年生
cs.56 <- csnc[c("sid", "nc.g5", "cs.g5", "cs.c.g5", "cs.d45")]
cvr.56 <- g37.msd[c("sid", "avg.45", "avg.56", "cvr.56")]
cs.cvr.56<-na.omit(data.frame(dplyr::inner_join(cs.56, cvr.56, by = "sid")))
# 6-7年生
cs.67 <- csnc[c("sid", "nc.g6", "cs.g6", "cs.c.g6", "cs.d56")]
cvr.67 <- g37.msd[c("sid", "avg.56", "avg.67", "cvr.67")]
cs.cvr.67<-na.omit(data.frame(dplyr::inner_join(cs.67, cvr.67, by = "sid")))学級規模と変動係数の散布図を描いてみる
#plot(cs.cvr.12$cs.g2, cs.cvr.12$cvr.12, xlim = c(0, 50), ylim = c(0,3), main = "cs.cvr.23")
plot(cs.cvr.45$cs.g4, cs.cvr.45$cvr.45, xlim = c(0, 50), ylim = c(0,3), main = "cs.cvr.45")
plot(cs.cvr.56$cs.g5, cs.cvr.56$cvr.56, xlim = c(0, 50), ylim = c(0,3), main = "cs.cvr.56")
plot(cs.cvr.67$cs.g6, cs.cvr.67$cvr.67, xlim = c(0, 50), ylim = c(0,3), main = "cs.cvr.67")
学級規模の変動と変動係数の散布図を描いてみる
plot(cs.cvr.45$cs.d34, cs.cvr.45$cvr.45, xlim = c(-15, 15), ylim = c(0,3), main = "cs_d.cvr.45")
plot(cs.cvr.56$cs.d45, cs.cvr.56$cvr.56, xlim = c(-15, 15), ylim = c(0,3), main = "cs_d.cvr.56")
plot(cs.cvr.67$cs.d56, cs.cvr.67$cvr.67, xlim = c(-15, 15), ylim = c(0,3), main = "cs_d.cvr.56")
以下のことを検討する
- 変動係数は学級規模で説明されるのか
- 変動係数は，prior achievementで説明されるのか
- 変動係数の大きさに対する(a)と(b)の交互作用は見られるか
# 学級規模の中心化
cs.cvr.45$cs.c.g4 <- cs.cvr.45$cs.g4 - mean(cs.cvr.45$cs.g4)
cs.cvr.56$cs.c.g5 <- cs.cvr.56$cs.g5 - mean(cs.cvr.56$cs.g5)
cs.cvr.67$cs.c.g6 <- cs.cvr.67$cs.g6 - mean(cs.cvr.67$cs.g6)
# Prior achievementの中心化
cs.cvr.45$avg.c.34 <- cs.cvr.45$avg.34 - mean(cs.cvr.45$avg.34)
cs.cvr.56$avg.c.45 <- cs.cvr.56$avg.45 - mean(cs.cvr.56$avg.45)
cs.cvr.67$avg.c.56 <- cs.cvr.67$avg.56 - mean(cs.cvr.67$avg.56)
head(cs.cvr.45)## sid nc.g4 cs.g4 cs.c.g4 cs.d34 avg.34 avg.45 cvr.45
## 38 18050 3 26.00000 3.69444444 0.00 50.22535 53.09859 0.8776247
## 39 18051 2 25.50000 3.19444444 0.50 52.68750 51.91667 1.0797116
## 40 18052 3 22.33333 0.02777778 0.00 49.35000 50.95000 0.6842961
## 41 18053 1 25.00000 2.69444444 1.00 56.65217 56.69565 0.8896116
## 56 18068 2 24.50000 2.19444444 -0.50 53.80435 50.13043 1.2757238
## 61 18073 4 26.25000 3.94444444 0.25 52.89474 52.51579 0.9930003
## avg.c.34
## 38 -2.72537856
## 39 -0.26323068
## 40 -3.60073068
## 41 3.70144324
## 56 0.85361715
## 61 -0.05599383Prior achievementと変動係数の散布図を描いてみる
plot(cs.cvr.45$avg.c.34, cs.cvr.45$cvr.45, xlim = c(-15, 15), ylim = c(0,3), main = "Prior_3, cvr.45")
plot(cs.cvr.56$avg.c.45, cs.cvr.56$cvr.56, xlim = c(-15, 15), ylim = c(0,3), main = "Prior_4, cvr.56")
plot(cs.cvr.67$avg.c.56, cs.cvr.67$cvr.67, xlim = c(-15, 15), ylim = c(0,3), main = "Prior_5, cvr.56")
回帰分析をしてみる
# 4年生終了時
res.45 <- brm(cvr.45 ~ cs.c.g4 + avg.c.34 + cs.c.g4:avg.c.34,
data =cs.cvr.45,
prior = c(set_prior("normal(0,10)", class = "b")),
chains = 4,
iter = 10000,
warmup = 3000
)## Compiling the C++ model## Start sampling##
## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 1).
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## Chain 4:print(res.45, digits = 3)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: cvr.45 ~ cs.c.g4 + avg.c.34 + cs.c.g4:avg.c.34
## Data: cs.cvr.45 (Number of observations: 48)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 0.954 0.039 0.876 1.032 29327 1.000
## cs.c.g4 0.005 0.006 -0.007 0.017 28634 1.000
## avg.c.34 0.021 0.012 -0.001 0.044 30946 1.000
## cs.c.g4:avg.c.34 -0.001 0.002 -0.006 0.003 34772 1.000
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 0.252 0.028 0.204 0.313 24914 1.000
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).# 5年生終了時
res.56 <- brm(cvr.56 ~ cs.c.g5 + avg.c.45 + cs.c.g5:avg.c.45,
data =cs.cvr.56,
prior = c(set_prior("normal(0,10)", class = "b")),
chains = 4,
iter = 10000,
warmup = 3000
)## Compiling the C++ model## recompiling to avoid crashing R session## Start sampling##
## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 1).
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## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 4).
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## Chain 4:print(res.56, digits = 3)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: cvr.56 ~ cs.c.g5 + avg.c.45 + cs.c.g5:avg.c.45
## Data: cs.cvr.56 (Number of observations: 117)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 1.042 0.019 1.005 1.079 27390 1.000
## cs.c.g5 0.002 0.003 -0.003 0.007 32434 1.000
## avg.c.45 0.022 0.006 0.009 0.035 25293 1.000
## cs.c.g5:avg.c.45 -0.001 0.001 -0.003 0.001 35415 1.000
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 0.198 0.013 0.174 0.226 25452 1.000
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).# 6年生終了時
res.67 <- brm(cvr.67 ~ cs.c.g6 + avg.c.56 + cs.c.g6:avg.c.56,
data =cs.cvr.67,
prior = c(set_prior("normal(0,10)", class = "b")),
chains = 4,
iter = 10000,
warmup = 3000
)## Compiling the C++ model## recompiling to avoid crashing R session## Start sampling##
## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 3.5e-05 seconds
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## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'd35359081d7733aebc9e00ac9119bde7' NOW (CHAIN 4).
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## Chain 4:print(res.67, digits = 3)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: cvr.67 ~ cs.c.g6 + avg.c.56 + cs.c.g6:avg.c.56
## Data: cs.cvr.67 (Number of observations: 167)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 1.055 0.015 1.026 1.085 21219 1.000
## cs.c.g6 -0.002 0.002 -0.007 0.002 28474 1.000
## avg.c.56 0.020 0.005 0.010 0.029 21128 1.000
## cs.c.g6:avg.c.56 0.001 0.001 -0.000 0.002 32593 1.000
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 0.186 0.010 0.167 0.208 19298 1.000
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).