https://mtaniguchiking.github.io/M4MD-forecast-docs-dev/tags/parameterizations/Recent content in Parameterizations on Models for missing dataHugoen-ushttps://mtaniguchiking.github.io/M4MD-forecast-docs-dev/posts/stratum-varying-fixed-effects/Mon, 01 Jan 0001 00:00:00 +0000https://mtaniguchiking.github.io/M4MD-forecast-docs-dev/posts/stratum-varying-fixed-effects/<p>Assume we have three strata, <link rel="stylesheet" href="https://mtaniguchiking.github.io/M4MD-forecast-docs-dev/katex/katex.min.css" /> <script defer src="https://mtaniguchiking.github.io/M4MD-forecast-docs-dev/katex/katex.min.js"></script> <script defer src="https://mtaniguchiking.github.io/M4MD-forecast-docs-dev/katex/auto-render.min.js" onload="renderMathInElement(document.body);"></script><span> \(s_0\) </span> , <span> \(s_1\) </span> , and <span> \(s_2\) </span> , where <span> \(s_0\) </span> is the &ldquo;reference&rdquo; stratum – in other words, <span> \(s_0\) </span> is the stratum for which the 0/1 indicator is 0 across the board in the indicator matrix below (the first row):</p> <span> \[\begin{bmatrix} 1 &amp; 0 &amp; 0 \\ 1 &amp; 1 &amp; 0 \\ 1 &amp; 0 &amp; 1 \end{bmatrix}\] </span> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-R" data-lang="R"><span style="display:flex;"><span>B_0 <span style="color:#f92672">+</span> (B_1 <span style="color:#f92672">+</span> B_1_s1_offset <span style="color:#f92672">*</span> s1 <span style="color:#f92672">+</span> B_1_s2_offset <span style="color:#f92672">*</span> s2) <span style="color:#f92672">*</span> x_1 </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#75715e"># in stratum s0</span> </span></span><span style="display:flex;"><span>B_0 <span style="color:#f92672">+</span> (B_1) <span style="color:#f92672">*</span> x_1 </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#75715e"># in stratum s1</span> </span></span><span style="display:flex;"><span>B_0 <span style="color:#f92672">+</span> (B_1 <span style="color:#f92672">+</span> B_1_s1_offset <span style="color:#f92672">*</span> s1) <span style="color:#f92672">*</span> x_1 </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#75715e"># in stratum s2</span> </span></span><span style="display:flex;"><span>B_0 <span style="color:#f92672">+</span> (B_1 <span style="color:#f92672">+</span> B_1_s2_offset <span style="color:#f92672">*</span> s2) <span style="color:#f92672">*</span> x_1 </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#75715e"># lm(y~x1*x2)</span> </span></span><span style="display:flex;"><span><span style="color:#a6e22e">model.matrix</span>(<span style="color:#f92672">~</span>x1<span style="color:#f92672">*</span>x2, <span style="color:#a6e22e">tibble</span>(x1 <span style="color:#f92672">=</span> <span style="color:#a6e22e">runif</span>(<span style="color:#ae81ff">5</span>), x2 <span style="color:#f92672">=</span> <span style="color:#a6e22e">runif</span>(<span style="color:#ae81ff">5</span>))) </span></span></code></pre></div>