# 1290 search results for "LaTex"

## Post 7: Sampling the item parameters with generic functions

October 10, 2013
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In this post, we will build the samplers for the item parameters using the generic functions developed in Post 5 and Post 6. We will check that the samplers work by running them on the fake data from Post 2, … Continue reading →

## That’s Smooth

October 10, 2013
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I had someone ask me the other day how to take a scatterplot and draw something other than a straight line through the graph using Excel.  Yes, it can be done in Excel and it’s really quite simple, but there are some limitations when using the stock Excel dialog screens. So it is probably in

## Some heuristics about spline smoothing

October 8, 2013
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$\mathbb{E}(Y\vert X=x)=h(x)$

Let us continue our discussion on smoothing techniques in regression. Assume that . where is some unkown function, but assumed to be sufficently smooth. For instance, assume that  is continuous, that exists, and is continuous, that  exists and is also continuous, etc. If  is smooth enough, Taylor’s expansion can be used. Hence, for which can also be writen as for...

## Some heuristics about local regression and kernel smoothing

October 8, 2013
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$\mathbb{E}(Y\vert X=x)=\beta_0+\beta_1 x$

In a standard linear model, we assume that . Alternatives can be considered, when the linear assumption is too strong. Polynomial regression A natural extension might be to assume some polynomial function, Again, in the standard linear model approach (with a conditional normal distribution using the GLM terminology), parameters can be obtained using least squares, where a regression of...

## Post 4: Sampling the person ability parameters

October 8, 2013
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The previous post outlined the general strategy of writing a MH within Gibbs sampler by breaking the code into two levels: a high level shell and a series of lower-level samplers which do the actual work. This post discusses the … Continue reading →

## Parallel Tempering in R with Rmpi

October 6, 2013
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$Parallel Tempering in R with Rmpi$

My office computer recently got a really nice upgrade and now I have 8 cores on my desktop to play with. I also at the same time received some code for a Gibbs sampler written in R from my adviser. I wanted to try a metropolis-coupled markov chain monte carlo, , algorithm on it to The post Parallel...

## Post 2: Generating fake data

October 6, 2013
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In order to check that an estimation algorithm is working properly, it is useful to see if the algorithm can recover the true parameter values in one or more simulated "test" data sets. This post explains how to build such … Continue reading →

## Post 1: A Bayesian 2PL IRT model

October 4, 2013
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In this post, we define the Two-Parameter Logistic (2PL) IRT model, derive the complete conditionals that will form the basis of the sampler, and discuss our choice of prior specification. We can find the appropriate values of numerically in R … Continue reading →

## The Uncertainty of Predictions

October 2, 2013
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There are many kinds of intervals in statistics.  To name a few of the common intervals: confidence intervals, prediction intervals, credible intervals, and tolerance intervals. Each are useful and serve their own purpose. I’ve been recently working on a couple of projects that involve making predictions from a regression model and I’ve been doing some

## Book example – iterative function systems for generating fractals

October 1, 2013
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$Book example – iterative function systems for generating fractals$

A number of people suggested that my book, Modeling Data With Functional Programming In R, be more upfront with examples …Continue reading »