Alternative Equation Formats

The equation on this page is available in multiple formats. Depending on your browser, some formats might not render correctly.

MathML

\begin{aligned} N & = # subjects (NTOTAL) \\ K & = # predictors (not counting intercept) \\ x & = (x_{1}, \dots, x_{K})^{'} = random variables for predictor vector \\ x_{- 1} & = (x_{2}, \dots, x_{K})^{'} \\ μ & = (μ_{1}, \dots, μ_{K})^{'} = E x = mean predictor vector \\ x_{i} & = (x_{i 1}, \dots, x_{i K})^{'} = predictor vector for subject i (i \in 1, \dots, N) \\ Y & = random variable for response (0 or 1) \\ Y_{i} & = response for subject i (i \in 1, \dots, N) \\ p_{i} & = P r o b (Y_{i} = 1 | x_{i}) (i \in 1, \dots, N) \\ ϕ & = P r o b (Y_{i} = 1 | x_{i} = μ) (RESPONSEPROB) \\ U_{j} & = unit change for j th predictor (UNITS) \\ {O R}_{j} & = O d d s (Y_{i} = 1 | x_{i j} = c) / O d d s (Y_{i} = 1 | x_{i j} = c - U_{j}) (c arbitrary, i \in 1, \dots, N, \\ j \in 1, \dots, K) (TESTODDSRATIO if j = 1, COVODDSRATIOS if j > 1) \\ Ψ_{0} & = intercept in full model (INTERCEPT) \\ Ψ & = (Ψ_{1}, \dots, Ψ_{K})^{'} = regression coefficients in full model \\ (Ψ_{1} = TESTREGCOEFF, others = COVREGCOEFFS) \\ ρ & = C o r r (x_{- 1}, x_{1}) (CORR) \\ c_{j} & = # distinct possible values of x_{i j} (j \in 1, \dots, K) (for any i) (NBINS) \\ x_{g j}^{⋆} & = g th possible value of x_{i j} (g \in 1, \dots, c_{j}) (j \in 1, \dots, K) \\ (for any i) (VARDIST) \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} N & = \# \text {subjects}\quad (\text {NTOTAL}) \\ K & = \# \text {predictors (not counting intercept)} \\ \mb{x} & = (x_{1}, \ldots , x_{K})' = \text {random variables for predictor vector} \\ \mb{x}_{-1} & = (x_{2}, \ldots , x_{K})' \\ \bmu & = (\mu _{1}, \ldots , \mu _{K})' = \mr{E}\mb{x} = \text {mean predictor vector} \\ \mb{x}_ i & = (x_{i1}, \ldots , x_{iK})' = \text {predictor vector for subject } i \quad (i \in 1, \ldots , N) \\ Y & = \text {random variable for response (0 or 1)} \\ Y_ i & = \text {response for subject } i \quad (i \in 1, \ldots , N) \\ p_ i & = \mr{Prob} (Y_ i = 1 | \mb{x}_ i) \quad (i \in 1, \ldots , N) \\ \phi & = \mr{Prob} (Y_ i = 1 | \mb{x}_ i = \bmu ) \quad (\text {RESPONSEPROB}) \\ U_ j & = \text {unit change for }j\text {th predictor} \quad (\text {UNITS})\\ \mr{OR}_ j & = \mr{Odds} (Y_ i = 1 | x_{ij} = c) / \mr{Odds} (Y_ i = 1 | x_{ij} = c - U_ j) \quad (c \text { arbitrary}, i \in 1, \ldots , N, \\ & \quad j \in 1, \ldots , K)\quad \text {(TESTODDSRATIO if }j = 1, \text {COVODDSRATIOS if }j > 1) \\ \Psi _0 & = \text {intercept in full model (INTERCEPT)} \\ \bPsi & = (\Psi _1, \ldots , \Psi _ K)' = \text {regression coefficients in full model} \\ & \quad (\Psi _1 = \text {TESTREGCOEFF, others = COVREGCOEFFS}) \\ \rho & = \mr{Corr}(\mb{x}_{-1}, x_1) \quad (\text {CORR}) \\ c_ j & = \# \text {distinct possible values of } x_{ij} \quad (j \in 1,\ldots , K) (\text {for any }i) \quad (\text {NBINS}) \\ x^\star _{gj}& = g\text {th possible value of } x_{ij} \quad (g \in 1, \ldots , c_ j) (j \in 1, \ldots , K) \\ & \quad (\mbox{for any }i) \quad (\mbox{VARDIST}) \\ \end{align*}