Search Results for: weighted mean

If the posterior distribution is a known distribution, then our work is greatly simplified. This is especially true when both the prior and posterior come from the same distribution family. A prior with this property is called a conjugate prior (with respect to the distribution of the data). We now consider the case where the … Read More

We show how to build a Rasch model via the following example. The approach described is based on the UCON method (i.e. unconditional maximum likelihood estimation using Newton’s Method). Example Example 1: Nine students (subjects) took a test consisting of the same 10 questions (items). Whether each student answered each of the questions correctly is … Read More

When data is missing in a time series, we can use some form of imputation or interpolation to impute a missing value. In particular, we consider the approaches described in Figure 1. Numeric label Text label Imputation type 0 linear linear interpolation 1 spline spline interpolation 2 prior use prior value 3 next use next … Read More

Basic Concepts Certain measures of central tendency are more robust to outliers than others (e.g. the median is more robust than the mean). We now look at a class of statistics, the M-estimators, that serve as candidates for robust measures of central tendency. In particular, we consider two such estimators:  Tukey’s biweight estimator and Huber’s … Read More

Basic Concepts Suppose that we have data (x11, …, x1k, y1), …, (xn1, …, xnk, yn), where for each i, yi is the mean value of y for all samples whose independent variables have the values xi1, …, xik and σi is the standard deviation of these samples. Now we convert the usual linear regression into … Read More

Basic Concepts Suppose the variances of the residuals of an OLS regression are known, i.e. var(εi) = σi2. When we assume homogeneity of variances, then there is a constant σ such that σi2 = σ2 for all i. When this is not so, we can use WLS regression with the weights wi = 1/σi2 to arrive at a better … Read More

The following is a summary of the Regression and ANOVA worksheet functions provided in the Real Statistics Resource Pack. These functions are organized into the following categories: Linear Regression Heteroskedasticity Autocorrelation Regression Power and Sample Size Stepwise Regression Exponential Regression Polynomial Regression Least Absolution Deviation (LAD) Regression Deming Regression Total Least Squares Regression Passing-Bablok Regression … Read More