Hi All, I have the below data on a “Diversity Index” over time for a given population of people:   Year Diversity Index 2005 35% 2006 36% 2007 37% 2008 38% 2009 39% 2010 38% 2011 40%     Per the census website, the DI: “the DI tells us the chance that two people chosen at random will be from different racial and ethnic groups….The DI is bounded between 0 and 1, with a zero-value indicating that everyone in the population has the same racial and ethnic characteristics, while a value close to 1 indicates that everyone in the population has different characteristics.” (full definition below)   I’d like to: 1) determine if there is a statistically significant upward trend in the index over time for this population, and 2) plot the data and show CIs around the estimates. Questions: 1) Would beta regression work for this, with the DI as the dependent variable and year as the independent variable? This seems to be a “continuous proportion” v. a “count proportion.” We don’t have a value of DI per person, it is one value for a group of people. 2) Some of the same people would be in the DI in different years. Should this be taken into account? If so, how – e.g., robust standard errors in a beta regression? Doesn't seen obvious as again, it's a value only calculated for a population and not an individual.     EQUATION BELOW:     Diversity Index Equation    DI = 1 – (H² + W² + B² + AIAN² + Asian² + NHPI² + SOR² + Multi²)    H is the proportion of the population who are Hispanic or Latino. W is the proportion of the population who are White alone, not Hispanic or Latino. B is the proportion of the population who are Black or African American alone, not Hispanic or Latino. AIAN is the proportion of the population who are American Indian and Alaska Native alone, not Hispanic or Latino. Asian is the proportion of the population who are Asian alone, not Hispanic or Latino. NHPI is the proportion of the population who are Native Hawaiian and Other Pacific Islander alone, not Hispanic or Latino. SOR is the proportion of the population who are Some Other Race alone, not Hispanic or Latino. MULTI is the proportion of the population who are Two or More Races, not Hispanic or Latino.   Source: https://www.census.gov/library/visualizations/interactive/racial-and-ethnic-diversity-in-the-united-states-2010-and-2020-census.html       ... View more