search for: theta_i

...$N$ indexes the total number of individuals, $K$ indexes the total number of items, $p(x|\theta,\beta)$ is the data likelihood and $f(\theta)$ is a population distribution. For the rasch model, the data likelihood is: \begin{equation} p(x|\theta,\beta) = \prod^N_{i=1}\prod^K_{j=1} \Pr(x_{ij} = 1 | \theta_i, \beta_j)^{x_{ij}} \left[1 - \Pr(X_{ij} = 1 | \theta_i, \beta_j)\right]^{(1-x_{ij})} \end{equation} \begin{equation} \label{rasch} \Pr(x_{ij} = 1 | \theta_i, \beta_j) = \frac{1}{1 + e^{-(\theta_i-\beta_j)}} \quad i = (1, \ldots, K); j = (1, \ldots, N) \end{equation} \noindent where $\theta_i$ is th...

Hello everybody. I am trying to cluster circular data (data points which are angles), thus i can not use the "dist" function in "mclust" to generate my distance matrix, I am using the function " Dij = 0.5*( 1 - cos(theta_i - theta_j)). The thing is "hclust" will not accept this distance matrix, i tried to put it in a data frame, but again i get an error message saying " Error in if (n < 2) stop("must have n >= 2 objects to cluster") : argument is of length zero". The distance matri...

...a + exp(-hL)y_t+ eta_{t+h}. The problem is that the distribution of the innovations of the transition equation depend on the previous value of the state variable. To be exact: y_t|y_{t-1} ~N(mu, Q_t) where Q is a diagonal matrix with elements equal to Q_{i,t} = sigma_i*(1-exp(-kappa_i*h)/kappa_i*(theta_i/2*(1-exp(kappa_i*h)+exp(-kappa_i*h)y_{t-1,i} The fkf returns the filtered states variables so y_{t-1,i} is available. I just can't figure out how to write my program in such a way that this information is included and updated in the state space model for each iteration in optim. Any suggestio...

...... 0 . . . ... 0 . . . ... 0 . . . ... 0 0 0 0 ... 1 and c_i as (-1,0,...,0). Then whatever value \beta_0 takes, the first value of u_i%*%theta_i is always zero, which automatically is larger than -1. That is how I construct u_i and c_i. contrOptim returns the barrier.value. I am wondering whether the value corresponds to -1*\mu*(\sum_{i=1}^p log(\hat{\beta_i}-0)+\log(1)). I need to get the information matrix which also takes into accoun...

I am relatively new to R, so this may be a much simpler question than it seems to me. I am trying to create a function that includes two summations, and can't figure out how. I am attaching the equation as a pdf file. This function will then be optimized over a chosen range of values, but right now I just need help with the function. Thank you. Zack Darnell Duke University -- Zack