Table 1 Two ways to display data with a multiclass response and predictors
From: Multiclass analysis and prediction with network structured covariates
Data Displayed With Class Label Used | Without Distinguishing Class Label | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
Class | Subject | Predictor | Response | Subject | Predictor | Response | |||||
1 | 1 | X 111 | X 211 | ⋯ | X p11 | Y11=1 | 1 | X ·11 | ⋯ | X ·1 p | Y ·1 |
2 | X 112 | X 212 | ⋯ | X p12 | Y12=1 | 2 | X ·21 | ⋯ | X ·2 p | Y ·1 | |
3 | X 113 | X 213 | ⋯ | X p13 | Y13=1 | 3 | X ·31 | ⋯ | X ·3 p | Y ·3 | |
⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | |
n 1 | \(X_{11n_{1}}\) | \(X_{21n_{1}}\) | ⋯ | \(X_{p1n_{1}}\) | \(Y_{1n_{1}} = 1\) | n 1 | \(X_{\cdot n_{1}1}\) | ⋯ | \(X_{\cdot n_{1} p}\) | \(Y_{\cdot n_{1}}\) | |
2 | 1 | X 121 | X 221 | ⋯ | X p21 | Y21=2 | n1+1 | \(X_{\cdot, n_{1}+1,1}\) | ⋯ | \(X_{\cdot, n_{1}+1, p}\) | \(Y_{\cdot, n_{1}+1}\) |
2 | X 122 | X 222 | ⋯ | X p22 | Y22=2 | n1+2 | \(X_{\cdot, n_{1}+2,1}\) | ⋯ | \(X_{\cdot, n_{1}+2, p}\) | \(Y_{\cdot, n_{1}+2}\) | |
3 | X 123 | X 223 | ⋯ | X p23 | Y23=2 | n1+3 | \(X_{\cdot, n_{1}+3, 1}\) | ⋯ | \(X_{\cdot, n_{1}+3, p}\) | \(Y_{\cdot, n_{1}+3}\) | |
⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | |
n 2 | \(X_{12n_{2}}\) | \(X_{22n_{2}}\) | ⋯ | \(X_{p2n_{2}}\) | \(Y_{2n_{2}} = 2\) | n1+n2 | \(X_{\cdot, n_{1}+n_{2},1}\) | ⋯ | \(X_{\cdot, n_{1}+n_{2}, p}\) | \(Y_{\cdot, n_{1}+n_{2}}\) | |
⋮ | ⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ |
I | 1 | X 1 I1 | X 2 I1 | ⋯ | X pI1 | YI1=I | n−nI+1 | \(X_{\cdot, n-n_{I}+1,1}\) | ⋯ | \(X_{\cdot, n-n_{I}+1, p}\) | \(Y_{\cdot, n-n_{I}+1}\) |
2 | X 1 I2 | X 2 I2 | ⋯ | X pI2 | YI2=I | n−nI+2 | \(X_{\cdot, n-n_{I}+2,1}\) | ⋯ | \(X_{\cdot, n-n_{I}+2, p}\) | \(Y_{\cdot, n-n_{I}+2}\) | |
3 | X 1 I3 | X 2 I3 | ⋯ | X pI3 | YI3=I | n−nI+3 | \(X_{\cdot, n-n_{I}+3,1}\) | ⋯ | \(X_{\cdot, n-n_{I}+3, p}\) | \(Y_{\cdot, n-n_{I}+3}\) | |
⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | ⋮ | ⋮ | ⋯ | ⋮ | ⋮ | |
n I | \(X_{1In_{I}}\) | \(X_{2In_{I}}\) | ⋯ | \(X_{pIn_{I}}\) | \(Y_{In_{I}} = I\) | n | X ·, n,1 | ⋯ | X ·, n,p | Y ·, n | |