search for: epsilon_

Hi all, I have some difficulties with the lme function and so this is my problem. Supoose i have the following model y_(ijk)=beta_j + e_i + epsilon_(ijk) where beta_j are fixed effects, e_i is a random effect and epsilon_(ijk) is the error. If i want to estimate a such model, i execute >lme(y~vec.J , random~1 |vec .I ) where y is the vector of my data, vec.J is a factor object and vec.I is the vector for the i indice. Now , this is...

...anywhere else. I will frame it in the context of an R related issue. To illustrate the problem, consider student achievement test score data with multiple observations available for each student. One way of modeling these data might be Y_{ti} = (\mu + \mu_{i} ) + (\beta_0 + \beta_{i} )*(time) + \epsilon_{ti} ; t indexes time and i indexes student The nlme code is tt<-lme(reponse~time, data, random=~time|ID) With this, I can extract the growth rate for each individual in the data set. Conceptually this is the sum of the main effect for time plus the empirical bayes estimate for each individua...

...ted standard errors) from identical models fit to different data sets. I would like to use these results to create pooled estimated regression coefficients and estimated standard errors for these pooled coefficients. In particular, I would like to estimate the model \beta_{i} = \mu + \eta_{i} + \epsilon_{i} \eta_{i} ~ iid N(0,\tau^2) and independent of the \epsilon_{i}, the latter themselves being independent with variances assumed known and equal to the squared standard errors reported in the regression output. I would like to use lme() to estimate \tau^2 by REML, and also get a sensibly weighte...

Hello - Here's what I'm trying to do. I want to fit a time series y with ARMA(1,1) + GARCH(1,1), there are also an exogeneous variable x which I wish to include, so the whole equation looks like: y_t - \phi y_{t-1} = \sigma_t \epsilon_t + \theta \sigma_{t-1} \epsilon_{t-1} + c x_t where \epsilon_t are i.i.d. random variables \sigma_t^2 = omega + \alpha \sigma_{t-1}^2 + \beta y_{t-1}^2 I looked through documentation of garchFit() from the fGarch library but didn't find a way to include exogeneous variables like x_t...

...us, does not use the cluster function option. This difference does not appear to be documented in the V&R `R Complements' file. I have data which is divided into 6 groups The lme model is of the form (simplified from the actual model a bit) y = a + b x_{ij} + \alpha_i + \beta_i x_{ij} + \epsilon_{ij} i = 1,...,6. where a and b are fixed effects and \alpha and \beta are random effects. I have a vector of the form clus = (1,1,1,2,5,6,4,4,4,3,...)' where the 1, 2 3 are all factors corresponding to different groups (or clusters in Splus terminology). In Splus I would use the argument...

Hey, I'm trying to implement a GARCH model with Johnson-Su innovations in order to simulate returns of financial asset. The model should look like this: r_t = alpha + lambda*sqrt(h_t) + sqrt(h_t)*epsilon_t h_t = alpha0 + alpha1*epsilon_(t-1)^2 + beta1 * h_(t-1). Alpha refers to a risk-free return, lambda to the risk-premium. I've implemented it like this: #specification of the model spec = ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,1), submodel = NULL, exter...

...x1 is a two level factor; x2 and x3 are continuous. We are including random intercepts for YEAR and SITE. On subject-matter considerations, we are also including a random coefficient for x3 within YEAR. Neglecting the log link, the model is y_{i,j} = x'_i \beta + \eta_i + z'_i \phi_j + \epsilon_{i,j} where i indexes SITE and j indexes YEAR, \beta is the vector of fixed effects \eta_i in the random intercept for SITE and \phi_j are the random intercept and coefficient for YEAR. I have written x'_i because the covariates are assumed (reasonably) to be constant over the 5 years...

...bb 0.925 2 pp 0.971 2 pb 1.051 2 bb 0.952 3 pp 0.927 3 pb 0.891 3 bb 0.892 4 pp 0.971 4 pb 1.010 4 bb 0.955 The model used for ANOVA in the book is Y_{ij} = \mu + \alpha_i + B_i + [(\alpha B)_{ij}] + \epsilon_{ij} (I am not quite confident how to represent this model in R, see below) The ANOVA table from S&R looks like this: MSB series 3 0.021 0.007 10.23 ** MSA genotypes 2 0.010 0.005 6.97 * MSE error 6 0.004 0.001 In R, I am using the following model (is...

...; to reflect a certain psychometric problem that occurs in longitudinal analyses of student achievement scores. These data are then analyzed using a linear model to obtain parameter estimates. This is replicated 250 times. For example, the model equation used is Y_{ti} = \mu + \beta \cdot t + \epsilon_{ti} So, I obtain 250 estimates of \mu and \beta. I take the standard deviation of these estimates to get the sampling distribution of the parameter (standard errors). Next, I take a single data set, contaminate the scores, and then use the analytical approach to obtain standard errors. So, I end u...

...jects each with 5 observations Y_t = (t_1, ..., t_5). Consider these 'longitudinal' data. So, I use reshape to put into the long format in order to regress the observations onto time, a time-varying covariate. I do the regression for each individual separately: Y_{t} = \mu + \beta(time) + \epsilon_{t} To get the statistic of interest (sigma_theta), I do the following with the original data: theta <- numeric(10) sigma <- numeric(10) for(i in 1:10){ tmp <- subset(long, ID==i) tmp.lm <- lm(obs ~ time, tmp) theta[i] <- coef(tmp.lm)[2] sigma[i] <- sum...

Hey, Does anyone know of an equivalent to the LaTeX \perp (perpendicular) symbol for adding to R plots? Parallel is easy enough ("||"), but I haven't been able to find a way of adding perpendicular. The plotmath documentation doesn't mention how to do it, so I'm inclined to think that it doesn't exist - but surely there must be some way of achieving the desired result,