Theil command e8/2/2023 If \(p_j\) is the proportion of group \(j\) in the region and there are \(J\) total groups, then the formula for entropy ( \(E\)) is given by:Įntropy will be at its maximum value when the proportion \(p_j\) is the same for each group, and entropy will be at its minimum value of zero when the area is made up entirely of one group. This measure of diversity is called entropy and is based on the proportions of different groups within the area. In order to measure Theil’s H, one has to first calculate a measure of diversity for each sub-region and the total region. When Theil’s H equals one, there is no diversity in the subregions of a region, and when Theil’s H equals zero, the diversity in each subregion is equal to the overall diversity of the region. Theil’s H provides a measure of the diversity in areas within a region (e.g. tracts within a city, counties within a state), relative to the overall diversity of the region. Calculating Theil’s H for a single stateĪs an example, we are going to calculate a measure of segregation called the Information Theory Index or sometimes just Theil’s H, after its creator.The Most Important Rule: Check yourself before you wreck yourself.The binomial distribution as a data-generating process.Dichotomous Outcomes and The Binomial Distribution.The IID Violation and Robust Standard Errors.Interaction terms with two categorical variables.Interaction terms with multiple categories.Categorical and quantitative variables combined in a single model.Categorical variables with more than two categories.Including Categorical Variables as Predictors.How to read a table of regression results.Including more than two independent variables.Interpreting results in a multivariate OLS regression models.The Power of Controlling for Other Variables.How good is \(x\) as a predictor of \(y\)?.Adding an OLS regression line to a plot.Using the lm command to calculate OLS regression lines in R.The general procedure of hypothesis testing.Calculating the confidence interval for other sample statistics.Calculating the confidence interval for the sample mean.What can we do with the sampling distribution?.Central limit theorem and the normal distribution.The Concept of the Sampling Distribution.Scatterplot and Correlation Coefficient.Graphically examining differences in distributions.Percentiles and the Five Number Summary.Looking at the distribution of a quantitative variable.Looking at the distribution of a categorical variable.Observational Data, Experimental Thinking.
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