Authorea

Anisha Keshavan added I_changed_the_text_to__.tex over 8 years ago

Commit id: 152ecf595989559140145bcc45eff168e58ea61b

deletions | additions

I changed the text to clarify that $i$ refers to subjects, and the choice of weights for the disease contrast vector. The coefficients are 00, 10 and 20 because the last 0 denotes that these are the true, unobserved effect sizes. The text now reads: \textit{"We first defined the true, unobserved model for \textbf{subject $i$} at site $j$ as:} \begin{equation} U_{ij} = \beta_{00} + \beta_{10}X_{i,j} + \beta_{20}Z_{i,j} + \epsilon_{i,j} \end{equation} \textit{Where $U_{i,j}$ is the unobserved value of the regional brain volume of interest (without any effects from the scanner), and \textbf{$\beta_{00}, \beta_{10}$ and $\beta_{20}$ are the true, unobserved, effect sizes.} The covariates are $Z_{i,j}$, residuals are $\epsilon_{i,j}$, \textbf{and the contrast vector, $X_{i,j}$, is given the weights $X_{high}, X_{low} = 0.5,-0.5$ so that $\beta_{10}$ is computed as the average difference between the high and low groups}. For this derivation we assume an equal number of subjects observed at each site in the high and low groups with balanced covariates. $\epsilon$ is normally distributed with mean 0 and standard deviation $\sigma_0$."}