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‎17_Panel.ipynb‎

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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## 固定効果モデル"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### 説明"
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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## ダミー変数モデルとしての固定効果モデル"
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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## ランダム効果モデル"
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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## 相関ランダム効果モデル"
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"\n",
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"* $\\bar{x}_i=\\dfrac{1}{T}\\sum_{t=1}^Tx_{it}$は説明変数の平均\n",
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"* $\\gamma$は$a_i$と$x_{it}$の相関関係を捉える係数\n",
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"* $r_i$は説明変数$x_{it}$と相関しないと仮定，即ち，$\\text{Cov}\\left(r_i\\bar{x}_{it}\\right)$\n",
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"* $r_i$は説明変数$x_{it}$と相関しないと仮定，即ち，$\\text{Cov}\\left(r_i\\bar{x}_{it}\\right)=0$\n",
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"\n",
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"（式５）を（式１）に代入すると次式を得る。\n",
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"\n",
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},
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"source": [
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"（含意）\n",
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"* $\\text{Cov}\\left(r_i,\\bar{x}_{it}\\right)\\;\\Rightarrow\\;\\text{Cov}\\left(v_i,\\bar{x}_{it}\\right)$\n",
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"* $\\text{Cov}\\left(r_i,\\bar{x}_{it}\\right)=0\\;\\Rightarrow\\;\\text{Cov}\\left(v_i,\\bar{x}_{it}\\right)=0$\n",
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"* REモデルと同じ構造となっており，違いは$\\bar{x}_i$が追加されている。\n",
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" * `linearmodels`の`RandomEffects`モジュールが使える。\n",
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"* 次の結果が成立する。\n",
@@ -1301,7 +1306,7 @@
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"hidden": true
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},
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"source": [
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"もう一度，FE対RE検定を行ってみよう。検定統計量（Statistics）は減少したが，以前帰無仮説は高い優位性で棄却できる。"
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"もう一度，FE対RE検定を行ってみよう。検定統計量（Statistics）は減少したが，以前として帰無仮説は高い優位水準で棄却できる。"
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]
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},
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{
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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## モデルの比較"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### OLS"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### 比較表の作成"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### FD vs. FE"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### FE vs. RE"
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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## シミュレーション"
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{
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true
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"heading_collapsed": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"## 標準誤差の問題"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### 分散の確認"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"### 対処方法"
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"cell_type": "markdown",
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"metadata": {
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"heading_collapsed": true,
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"hidden": true
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"hidden": true,
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"jp-MarkdownHeadingCollapsed": true
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},
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"source": [
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"#### 説明と計算"
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.10"
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"version": "3.12.7"
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},
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"toc": {
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"base_numbering": 1,

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