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tables.tex
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\ctable[caption={Reparametrization for strong and weak heredity principle for \texttt{sail} model},label=tab:reparam,pos=h!,doinside=\footnotesize, ]{lll}{
}{
\FL
Type & Feature & Reparametrization \ML
\multicolumn{1}{m{3cm}}{Strong heredity} & \multicolumn{1}{m{6cm}}{$\hat{\btau}_{j} \neq 0 \textrm{ only if } \hat{\btheta}_j \neq 0 \tm{ and } \hat{\beta}_E \neq 0$} & $\btau_{j} = \gamma_{jE} \beta_E \btheta_j $ \\
\multicolumn{1}{m{3cm}}{Weak heredity} & \multicolumn{1}{m{6cm}}{$\hat{\btau}_{j} \neq 0 \textrm{ only if } \hat{\btheta}_j \neq 0 \tm{ or } \hat{\beta}_E \neq 0$} & $\btau_{j} = \gamma_{jE}(\beta_E \cdot \mb{1}_{m_j} + \btheta_j)$ \LL
}
% latex table generated in R 3.6.1 by xtable 1.8-4 package
% Thu Nov 14 17:01:43 2019
% latex table generated in R 3.6.1 by xtable 1.8-4 package
% Thu Nov 14 17:16:26 2019
%\multicolumn{#1}{c}{#2}
\vspace{-1in}
\begin{landscape}
\ctable[caption={\footnotesize Mean (standard deviation) of the number of selected variables ($|\widehat{\mathcal{J}}|$), true positive rate (TPR) and false positive rate (FPR) as a percentage from 200 simulations for each of the five scenarios. $|\mathcal{J}|$ is the number of truly associated variables.},label=tab:resultmultinom,pos=h,doinside=\scriptsize]{lcccccccccccccc}{
}{
\FL
& \mc{2}{Linear} & & \mc{2}{Linear} & & \mc{3}{Non-linear} & & \mc{3}{Non-linear} \NN
& \mc{2}{Main Effects} & & \mc{2}{Interactions} & & \mc{3}{Main Effects} & & \mc{3}{Interactions} \NN
\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-10}\cmidrule{12-14} % Important: no space before \cmidrule
& lasso & adaptive & & lassoBT & GLinternet & & HierBasis & SPAM & gamsel & & sail & adaptive & sail \NN
& & lasso & & & & & & & & & & sail & weak \ML
\mcl{3}{1a) Strong heredity ($|\mathcal{J}|=7$)} \\
$|\widehat{\mathcal{J}}|$ & 30 (14) & 8 (4) & & 37 (17) & 41 (21) & & 152 (28) & 38 (17) & 47 (19) & & 37 (15) & 8 (5) & 34 (13) \\
TPR & 54.9 (7.4) & 49.7 (10.4) & & 62.0 (10.4) & 66.7 (12.8) & & 66.2 (7.6) & 60.9 (9.0) & 57.1 (6.5) & & 90.6 (7.7) & 69.7 (28.8) & 86.4 (10.1) \\
FPR & 1.3 (0.7) & 0.2 (0.2) & & 1.6 (0.8) & 1.8 (1.0) & & 7.4 (1.4) & 1.7 (0.8) & 2.2 (0.9) & & 1.5 (0.7) & 1.1 (9.7) & 1.4 (0.6) \ML
\mcl{3}{1b) Weak heredity ($|\mathcal{J}|=5$)} \\
$|\widehat{\mathcal{J}}|$ & 19 (12) & 4 (2) & & 20 (13) & 37 (22) & & 23 (22) & 28 (15) & 22 (15) & & 16 (9) & 7 (6) & 17 (11) \\
TPR & 41.0 (4.5) & 40.2 (1.9) & & 41.0 (4.5) & 65.1 (15.2) & & 42.6 (6.7) & 54.8 (8.8) & 43.8 (7.9) & & 47.8 (10.4) & 46.9 (11.2) & 51.0 (12.8) \\
FPR & 0.8 (0.6) & 0.1 (0.1) & & 0.9 (0.7) & 1.7 (1.1) & & 1.1 (1.1) & 1.3 (0.7) & 1.0 (0.8) & & 0.7 (0.4) & 0.2 (0.3) & 0.7 (0.5) \ML
\mcl{3}{1c) Interactions Only ($|\mathcal{J}|=2$)}\\
$|\widehat{\mathcal{J}}|$ & 14 (13) & 3 (2) & & 15 (14) & 42 (21) & & 14 (14) & 14 (12) & 14 (13) & & 6 (7) & 3 (5) & 6 (7) \\
TPR & 0.0 (0.0) & 0.0 (0.0) & & 0.2 (3.5) & 82.6 (26.3) & & 0.0 (0.0) & 0.0 (0.0) & 0.0 (0.0) & & 0.0 (0.0) & 0.7 (5.9) & 0.0 (0.0) \\
FPR & 0.7 (0.6) & 0.6 (6.9) & & 0.8 (0.7) & 2.0 (1.1) & & 0.7 (0.7) & 0.7 (0.6) & 0.7 (0.6) & & 0.3 (0.4) & 0.2 (0.2) & 0.3 (0.4) \ML
\mcl{3}{2) Linear Effects ($|\mathcal{J}|=7$)}\\
$|\widehat{\mathcal{J}}|$ & 36 (16) & 8 (3) & & 48 (17) & 47 (20) & & 36 (17) & 42 (18) & 36 (16) & & 30 (12) & 12 (4) & 19 (14) \\
TPR & 69.9 (4.7) & 67.4 (6.7) & & 72.7 (6.6) & 92.6 (9.1) & & 69.9 (4.6) & 64.6 (8.4) & 69.9 (4.7) & & 87.4 (14.1) & 88.6 (13.5) & 64.3 (13.6) \\
FPR & 1.6 (0.8) & 0.2 (0.1) & & 2.1 (0.8) & 2.1 (1.0) & & 1.6 (0.9) & 1.9 (0.9) & 1.6 (0.8) & & 1.2 (0.6) & 0.3 (0.2) & 0.7 (0.7) \ML
\mcl{3}{3) Main Effects Only ($|\mathcal{J}|=5$)}\\
$|\widehat{\mathcal{J}}|$ & 30 (15) & 7 (4) & & 31 (15) & 35 (18) & & 160 (17) & 42 (18) & 54 (20) & & 40 (16) & 8 (5) & 40 (16) \\
TPR & 76.6 (10.0) & 67.4 (13.6) & & 77.0 (10.1) & 78.3 (8.8) & & 97.0 (7.5) & 92.3 (10.9) & 82.4 (10.0) & & 89.3 (13.0) & 78.0 (14.8) & 89.1 (13.0) \\
FPR & 1.3 (0.7) & 0.2 (0.2) & & 1.4 (0.8) & 1.6 (0.9) & & 7.8 (0.8) & 1.9 (0.9) & 2.5 (1.0) & & 1.8 (0.8) & 0.2 (0.2) & 1.8 (0.8) \LL
}
\end{landscape}
\ctable[caption={Comparison of analytic methods for selecting interactions using the Nurse Family Partnership program and the SUPPORT datasets. Averages (standard deviations in parentheses) are based on 200 bootstrap samples.},label=tab:rda,pos=h,doinside=\footnotesize, ]{lccccc}{\tnote{\texttt{GLinternet} results not reported for NFP data since the algorithm did not converge in many of the bootstrap samples.}\tnote[b]{$|\widehat{\mathcal{J}}|$ is the number of variables selected by the method.}
}{
\FL
& \multicolumn{2}{c}{Nurse Family Partnership} & &\multicolumn{2}{c}{SUPPORT} \NN
\cmidrule(r){2-3} \cmidrule(l){5-6}
Method & Mean Squared Error & $|\widehat{\mathcal{J}}|$ & & AUC & $|\widehat{\mathcal{H}}|$ \ML
\texttt{sail} & 3.5 (0.6) & 4 (3) & & 0.66 (0.01) & 25 (3) \NN
\texttt{lassoBT} & 3.53 (0.477) & 11 (6) & & 0.65 (0.009) & 49 (14) \NN
\texttt{GLinternet}\tmark & -- & -- & & 0.65 (0.009) & 58 (7) \LL
}