Trivariate Kernel Density Estimation of Spatiotemporal Crime Events with Case Study for Lithuania

Round 1

Reviewer 1 Report

Author Response

Thank you for your feedback. Here are our answers:

1- Did you develop a new method, as you said in the title of the paper?

We did not develop a new method but selected optimal KDE method using data-driven criteria. The title of the paper emphasizes the case study. 

2- If yes, what is the difference between your developed method with the same work which was developed by other researchers? e.g.:

As said above, no new principal methods were created. We rather developed a new framework for using existing methods from two areas: spatial point pattern and kernel density estimation:

• combinations of different existing KDE methods with different bandwidths were used;
• we suggested the use of spatial point processing residuals as a measure of internal training error in order to select optimal KDE surfaces that were generated using various KDE methods.

The study is similar to the one described in the paper by Y. Hu et al., A Spatio-temporal kernel density estimation framework for predictive crime hotspot mapping and evaluation. (ttps://doi.org/10.1016/j.apgeog.2018.08.001). However, Hu and co-authors used only one KDE method and one bandwidth selection method. They did not focus on evaluating the accuracy of KDE. But different bandwidth selection methods yield very different results in terms of bandwidth size. We used a range of different KDE variants and methods as well as spatial point processing residuals as an internal training error for testing KDE accuracy and for selection of the optimal bandwidth.

3- From an expert point of view, a method may be developed or invented that is valuable. But if that model cannot be used by a large part of scientists and other disciplines, I think it can be challenging and question its value. Have you provided a tool or script for the provided method to be used in the software? I believe that many articles are only formulated and understood by certain people and do not find practical use. For example, we use the MGWR method in GIS. We have the right tools. Wouldn't it be better to add a guide to the optimal model implementation to the article?
It can be used if a proper guide is provided. Your work is valuable. But in my money, most of published work are not usable and applicable. Because only the authors have understood how to implement it.

The proposed approach to bandwidth selection is based on the concept of internal validations. The findings are demonstrated and tested on bandwidth selectors and KD estimates of violent crime events in Lithuania, but the results can be applied to other datasets of events with spatial point patterns (e.g., traffic accidents, noninfectious diseases, mobile phone calls, animal sightings, trees in a forest, and many others.). Optimal density surfaces can be used in various applications and implementations may vary depending on the scope of application. In this article we did not plan to provide a generalized application methodology, but our code is available for re-use. R scripts are available upon request as now stated at the end of the Section 4.

Reviewer 2 Report

Review of Trivariate kernel density estimation of spatiotemporal crime events with case study for Lithuania

Overall, this is an advanced methodological piece that should inform geospatial researchers (and place-based criminologists) who examine concentrations of a phenomenon (in this case, crime). However, there are some suggestions that are needed before it is ready for publication in Sustainability. I detail these comments/suggestions below.

Minor Point: While there are parts of the manuscript that are well-written, it should be given another read for grammar/syntax/word choice issues before submitting a revision. For example, on line 292, “…2.78 million of records…”

I think the authors do a good job overall discussing the relevant literature on the method(s). However, I would like a “Present Study” section (or just a paragraph) that highlights how this study contributes to the existing body of relevant research. How is it different? How does it build on prior knowledge?

You mention that population density is highly correlated with violent crime. What other socio-demographic factors can the KDE factor in? For example, concentrated disadvantage, residential mobility, percentage of younger people in a given area may also be correlated with crime. How does KDE factor these variables in? Density of single-parent households, for example. Perhaps a limitation of the method noted at the end.

The final few paragraphs draw out key contributions of this study. But I would like to the authors speculate how this study informs various disciplines. What other rival methods would you speculate that trivariate KDE is better than?

Author Response

Thank you for your feedback. Here are our answers:

Minor Point: While there are parts of the manuscript that are well-written, it should be given another read for grammar/syntax/word choice issues before submitting a revision. For example, on line 292, “…2.78 million of records…”

The manuscript was consistently revised, and corrections were made, including line 292, "...2.78 million records..."

I think the authors do a good job overall discussing the relevant literature on the method(s). However, I would like a “Present Study” section (or just a paragraph) that highlights how this study contributes to the existing body of relevant research. How is it different? How does it build on prior knowledge?

The study builds on previous and current research in two areas: nonparametric kernel density estimation with its aspects of optimal bandwidth selection and the theory of point spatial pattern processes. These two areas of research are examined in sections 2 and 3 of the manuscript correspondingly.

The originality of the approach lies in using the Poisson process residuals to select the most efficient KDE. It is a simple practical approach to testing the performance of KDE methods which cannot be directly compared to each other using common measures of errors such as Integral Square Error and Mean Integrated Squared Error. The approach has been implemented and tested on a large data set.

You mention that population density is highly correlated with violent crime. What other socio-demographic factors can the KDE factor in? For example, concentrated disadvantage, residential mobility, percentage of younger people in a given area may also be correlated with crime. How does KDE factor these variables in? Density of single-parent households, for example. Perhaps a limitation of the method noted at the end.

There are many socio-demographic factors that could be used for estimation of relative risk surfaces using KDE method: population demographics, education, household income, employment, ethnic composition and others that the reviewer has listed.  Some of these factors are well known in the context of spatial criminology, some are only speculative about their links to violent crime. Often the factors are strongly correlated. Often there is a lack of objective data to reliably assess these links. If a factor is already known (usually from other studies) to have an impact on crime, and it is possible to obtain data at the necessary level of detail, this data could be used for estimation of KDE relative risk surfaces. Relative risk KDE analysis integrates a single additional factor, while nonparametric kernel regression KDE methods allow multiple factors. Selecting the optimal criteria in each case would require additional experimentation and is beyond the scope of this paper.

The final few paragraphs draw out key contributions of this study. But I would like to the authors speculate how this study informs various disciplines. What other rival methods would you speculate that trivariate KDE is better than?

In this manuscript, we did not aim to compare KDE with other parametric and nonparametric methods. The main goal was to show the performance of different variants of KDE and choose the KDE method based on the best estimates of the internal spatial point process residuals.

The results – density and intensity surfaces - can be used in a variety of applications and methods, including kernel regression, kernel discriminant analysis, trend dynamics estimation, density level set estimation, unsupervised and supervised learning, and density ridge estimation for PCA (Chacon and Duong , 2018).