UCLA

Traditional crime measures, such as crime counts and rates, effectively describe the overall volume of crime. However, they provide limited information about the composition of crime within local areas. This thesis examines whether a Crime Diversity Index (CDI) can add useful information about local crime patterns beyond conventional measures of crime volume. The analysis is based on 875,087 crime incidents reported by the Los Angeles Police Department (LAPD) between January 2020 and December 2023. These incidents are grouped into eight broad crime categories, and crime diversity is measured using a normalized Shannon Diversity Index. The main spatial unit used in the study is the LAPD Reporting District.The study examines crime diversity from spatial, temporal, and spatio-temporal perspectives. Spatial variation is evaluated using Reporting District-level comparisons, choropleth maps, and Global Moran's $I$. Temporal patterns are examined across months and seasons using descriptive statistics, one-way ANOVA, and a random-intercept mixed-effects sensitivity analysis. The relationship between crime volume and diversity is assessed using correlation and ordinary least squares regression, together with fixed-count repeated subsampling and spatial error regression to evaluate the effects of unequal incident counts and residual spatial dependence. Spatio-temporal dynamics are further examined across eight consecutive half-year periods.The results show substantial variation in crime diversity across Reporting Districts and statistically significant positive spatial autocorrelation. In the unadjusted data, crime diversity is strongly and positively associated with crime volume. However, when exactly 100 incidents are repeatedly sampled from each eligible Reporting District, the association between the count-adjusted CDI and original crime volume becomes negligible, while the relative CDI pattern across districts remains highly stable. Spatial error modeling further shows that residual spatial dependence is important in the count--diversity relationship. Temporal variation is more modest: monthly diversity remains relatively stable, and although seasonal differences are statistically detectable, their magnitude remains small after accounting for repeated observations within Reporting Districts. The half-year analysis shows that the broad spatial pattern of crime diversity persists over time while local changes remain visible.Overall, the findings indicate that crime diversity should not be interpreted independently of crime volume, particularly in low-volume areas. Nevertheless, the CDI captures a compositional dimension of local crime that is not reducible to total incident frequency. The results support using crime diversity as a complementary rather than competing measure of local crime patterns and provide a reproducible framework for jointly examining crime volume, crime composition, and their spatial and temporal variation in Los Angeles.