Linear Panel Analysis. Models of Quantitative Change

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To overcome these issues, we recommend that the data or meta-data on species-level changes be provided in a repository, either as online supplementary material in the journal or an institutional repository e. Table 2. This will assist interpretation of climate impacts and encourage re-analysis from different viewpoints. We suggest that the issues discussed in this review should be considered when planning and conducting analyses in climate change ecology, and also when interpreting the reliability of published results from other studies.

A summary of our suggestions is included below and are ordered roughly according to the sequence that they might be most useful. These suggestions are equally applicable to marine and terrestrial studies. Consider how spatial and temporal resolution of data will influence the strength of inferences about drivers of change. For example, long time series with frequent observations, over large regions and over multiple climate cycles provide an ideal basis for interpreting recent anthropogenic climate change. Longer term palaeo-ecological data can also provide valuable baselines for assessing climate impacts.

Formulate alternative hypotheses for causal relationships between the ecological and climate variables. In some cases, observational studies can be coupled with experimental studies that shed light on the mechanisms driving change. In formulating alternative hypotheses, consider important drivers of ecological change, such as climate variability, ecosystem dynamics, other anthropogenic drivers of change e. Where possible, data should be obtained on these drivers.

Identify response variables. Many different response variables may be derived from some datasets. The most statistically reliable response variables will generally have the largest sample size e. Non-conventional response variables may also reveal new patterns, such as considering changes in ecological variability rather than changes in the mean. Formulate the identified processes as a statistical model or a series of models. Ideally, the models will include all drivers of change identified in step 2. Where possible, model-based approaches should be used rather than data transformations.

Where temporal data cannot be obtained on key drivers, indirect approaches can be useful, such as comparisons among species. Furthermore, application of analytical methods beyond those traditionally used by ecologists i. Promising methods rarely used in ecology include tests of cointegration, wavelets for the analysis of ecological cycles and spatio-temporal models. Temporal autocorrelation should be considered in analysis if using time series data. Temporal autocorrelation patterns can often be reduced using filters, detrending or differencing. A more powerful approach for two variables can be to adjust the degrees of freedom in significance tests or to use a test of cointegration.

If multiple predictors may influence the response, autoregressive models may be used and also allow estimation of rates of change. Spatial autocorrelation and patterns should be considered if using spatial data. Spatial patterns can be ignored in analysis by grouping or averaging the data to a single value in space; however, this approach reduces the information content of the data. In some cases, meta-analysis, generalized additive models, mixed-effects models and geostatistics can be used to assist understanding the processes driving spatial patterns.

Where spatial non-independence of data points cannot be accounted for by using covariates, it can be modelled explicitly. For spatially continuous data, models of spatial autocorrelation or spatial covariates can be used to account for non-independence of data points. Mixed-effects models can be used for data collected at discrete sites. Metrics summarizing the rate-of-change for all species studied should be reported.

Species-level metrics assist the uptake of the results of a study by other researchers and help in building global understanding of marine climate impacts. Registering data with an online database is encouraged Table 2. Consideration of these suggestions should help climate change ecologists apply appropriate statistical approaches to their data and afford them some confidence in the robustness of their results. We hope that this work will also encourage the re-analysis of archived datasets using appropriate approaches. A solid statistical basis for climate change ecology will help advance policy debates on climate change, improve predictions of impacts and aid the development of strategies for adaptive management.

Clarke, N. Dulvy, S. Hawkins, C. Parmesan, F. Schwing and an anonymous reviewer provided useful comments and D. Hogan and S. Thompson assisted with database compilation. National Center for Biotechnology Information , U. Global Change Biology. Glob Chang Biol. Author information Article notes Copyright and License information Disclaimer. Christopher Brown, tel. Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2. Abstract Contemporary impacts of anthropogenic climate change on ecosystems are increasingly being recognized.

Introduction Although our knowledge of the impacts of anthropogenic climate change on biological systems is informed by the intersection of scientific theory, modelling, experiment and observation, it is only through observation that we can track the response of the biosphere to climate change. Assessment of current statistical approaches in climate change ecology We searched the peer-reviewed literature on climate change ecology for articles examining climate change impacts on the basis of observational studies.

Open in a separate window. Data requirements for assessing climate change impacts Strongest inferences on impacts of climate change require observational data that cover long time spans and large spatial scales Parmesan et al.

Associated Data

Comparing historical and contemporary data sets Baselines for assessing climate impacts for data-poor regions or taxa can be obtained by conducting surveys in sites where historical data are available and comparisons can be made between present and historical data. Retrospective data in climate impact studies Given the relative paucity of long biological and ecological time series, retrospective methods for obtaining data to test for impacts of climate change provide a rich and relatively untapped resource.

Addressing statistical issues A major challenge in statistical analysis is simultaneously minimizing risks of attributing causality to simple associative relationships and of missing relationships that are the result of real ecological processes. Accommodating multiple factors in analyses When investigating ecosystem change, a host of anthropogenic impacts including climate and natural dynamics are confounded, complicating interpretation and potentially leading to spurious conclusions when important drivers are not included in analysis.

Table 1 Summary of statistical approaches described in the text, with references, and appropriate routines in the free statistical package R. Statistical consideration Reasons to consider Statistical solutions Examples: climate change ecology References for methodology R guide Multiple factors influence response Ignoring multiple factors may result in attributing biological change to wrong driver or missing interactions Multiple regression, generalized multiple regression Dulvy et al.

NA, not available. Identifying spurious relationships and accounting for auto-correlation in biological data Temporal and spatial autocorrelation arise from non-independence of observations and are a common feature of time series and geographical studies Legendre et al. Modelling changes in variability, cycles and periods Most cases discussed so far have focussed on the effect of climate change on trends in ecological response variables. Metrics of phenology and distribution The interpretation of climate impacts may often be assisted by deriving metrics of biological responses from raw observations that are readily associated with climate change.

Community-wide studies A major strength of Fodrie et al. Table 2 Information on some online data repositories. Conclusions We suggest that the issues discussed in this review should be considered when planning and conducting analyses in climate change ecology, and also when interpreting the reliability of published results from other studies. Evidence for eutrophication of the Irish Sea over four decades. Limnology and Oceanography. Climate, plankton and cod. Reorganization of North Atlantic marine copepod biodiversity and climate.

Causes and projections of abrupt climate-driven ecosystem shifts in the North Atlantic. Ecology Letters. Rise and fall of jellyfish in the eastern Bering Sea in relation to climate regime shifts. Progress in Oceanography. On the relationship between abundance and distribution of species.

The American Naturalist. Regional warming-induced species shift in north-west Mediterranean marine caves. Environmental influences on long-term variability in marine plankton. Statistics: An Introduction Using R. Chichester: Wiley; Spatial autocorrelation and statistical tests: some solutions.

Journal of Agricultural, Biological, and Environmental Statistics. The importance of phylogeny to the study of phenological response to global climate change. Declining coral calcification on the Great Barrier Reef. Model-Based Geostatistics. New York: Springer; Uncertainty of detecting sea change. Climate change and deepening of the North Sea fish assemblage: a biotic indicator of warming seas. Journal of Applied Ecology. Impact of climate change on marine pelagic phenology and trophic mismatch. Multi-decadal oceanic ecological datasets and their application in marine policy and management.

Trends in Ecology and Evolution. Co-integration and error correction: representation, estimation and testing. Planktonic foraminifera of the Californian current reflect 20 th -century warming. Climate-related, decadal-scale assemblage changes of seagrass-associated fishes in the northern Gulf of Mexico. Contrasting population changes in sympatric penguin species in association with climate warming. Body size-dependent responses of a marine fish assemblage to climate change and fishing over a century-long scale. Structural Equation Modeling and Natural Systems.

Cambridge: Cambridge University Press; On the phenology of North Sea ichthyoplankton. Evidence for a multi-species coccolith volume change over the past two centuries: understanding a potential ocean acidification response. A global map of human impact on marine ecosystems. Conserving biodiversity under climate change: the rear edge matters.

Empirical evidence for North Pacific regime shifts in and The impacts of climate change in coastal marine systems. Detection of environmental change in a marine ecosystem — evidence from the western English Channel. The Science of the Total Environment. Impact of warming on abundance and occurrence of flatfish populations in the Bay of Biscay France Journal of Sea Research. The effect of spatial and temporal heterogeneity on the design and analysis of empirical studies of scale-dependent systems.

Module 10 - Single-level and multilevel models for nominal responses

Alternatives to statistical hypothesis testing in ecology: a guide to self teaching. Ecological Applications. The impact of climate change on the world's marine ecosystems. Spatial analysis shows that fishing enhances the climatic sensitivity of marine fishes. Canadian Journal of Fisheries and Aquatic Sciences.

Climate-driven changes in abundance and distribution of larvae of oceanic fishes in the southern Californian region. Climatic Changes in the Arctic in relation to Plants and Animals. Contributions to Special Scientific Meetings. Phytoplankton calcification in a high-CO2 world.

Climatic changes in the Arctic in relation to plants and animals. Evidence of a shift in the cyclicity of Antarctic seabird dynamics linked to climate. Long-term changes in migration timing of adult Atlantic salmon Salmo salar at the southern edge of the species distribution.

How to Choose the Right Forecasting Technique

Trophic amplification of climate warming. Introduction to modern time series analysis. Berlin: Springer; Spatial autocorrelation and the selection of simultaneous autoregressive models. Global Ecology and Biogeography. Numerical Ecology. New York: Elsevier; The consequences of spatial structure for the design and analysis of ecological field surveys.

Do distributional shifts of northern and southern species of algae match the warming pattern? Oscillating trophic control induces community reorganization in a marine ecosystem. Is the spread of the neophyte Spartina anglica enhanced by increasing temperatures? Aquatic Ecology. Long-term changes in the geographic distribution and population structures of Osilinus lineatus Gastropoda: Trochidae in Britian and Ireland. Testing and adjusting for publication bias. Effect of climate and overfishing on zooplankton dynamics and ecosystem structure: regime shifts, trophic cascades, and feedback loops in a simple ecosystem.

Phenological changes in intertidal con-specific gastropods in response to climate warming. Sea ice retreat alters the biogeography of the Bering Sea continental shelf. Changing spatial distribution of fish stocks in relation to climate and population size on the Northeast United States continental shelf. Marine Ecology Progress Series. CalCOFI in a changing ocean. A globally coherent fingerprint of climate change impacts across natural systems. Overstretching attribution.

Bloomsbury Collections - What is Quantitative Longitudinal Data Analysis?

However, there are some important new issues to consider in the interpretation and estimation of multilevel binary response models. In this module we consider the whole process of conducting a research project using multilevel modelling, taking as an example a study of ethnic differences in educational achievement and progress. The research process starts with the formulation of research questions as hypotheses that can be tested using multilevel models. The next step is to prepare the dataset for analysis, which includes decisions about issues such as coding variables, deriving new variables and handling missing data.

The analysis then begins with a detailed exploration of the data before fitting multilevel models, building model complexity gradually. We show how the research process is iterative with the results from initial analyses leading to refinements in the original research questions. This module builds on Module 5: Introduction to multilevel modelling.

Course modules You will need to register or log in to view the course. The aims of Module 1 are: To give a broad overview of how research questions might be answered through quantitative analysis. Such questions as the following are explored: How does quantitative analysis relate to other methods of inquiry?


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Why is it required and what sorts of evidence can it supply? To introduce the vocabulary of quantitative analysis and specify the common terminology to be used in later modules. Of particular importance is the operational definition of research concepts how we get from real world characteristics to numbers in our data set and how this leads to observable variables at different levels of measurement.

To introduce sources of data and concepts relating to how it may be possible to generalise results from samples of various kinds to the populations they are drawn from.

111 Simple Regression Model: Specification and Estimation_Lecture II

To discuss how variables are defined, what different types there are, and how this may influence how they are analysed. To give some emphasis to certain ideas such as the nature of variability or the recognition of hierarchical units of analysis that are central to multilevel modelling C 1. What questions might we ask? Intra annual trends associated with alcohol policy changes were modelled using marginal splines, and annual trends and seasonal changes in crime were captured using fractional polynomials and sine-cosine pairs also known as Fourier terms , representing a thorough consideration of temporal oscillations in criminal activity.

Four studies published prior to used hierarchical regression to simultaneously estimate the influence of alcohol outlet density, socio-economic factors [ 89 , 90 ] and their interactions [ 91 ] on the rate of violent crime across municipalities, accounting for both individual level frequency of drinking and driving with an intoxicated person and city wide alcohol outlet density alcohol consumption influences on youth drinking and driving [ 33 ].

SAR, CAR and SEM models address spatial dependence within the outcome or exploratory variables correlation of data between analysis units to avoid spatially clustered residuals and biased coefficients [ ]. Spatial lagged models SAR include a parameter of interest on the right hand side of the regression equation, calculated in some studies as the weighted average of alcohol outlets [ 16 , 57 ] or socio-demographics in neighbouring regions, to estimate the incidence crime.


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Whereas, the spatial error models SEM restrict autocorrelation to the error term assuming missing variable bias, effecting the covariance structure of the random disturbance term e. Frequently, spatial models use a contiguity spatial weights matrix to represents the dependency between values or errors at each location and adjacent locations among analysis units, though distance weighted matrices also exist.

CAR models, in contrast to SAR and SEM models, assume the state of a particular area is influenced by its neighbours and not neighbours of neighbours Markov property applying a symmetric weights matrix. Pursuant to the spatial models, two cross-section studies explored geographically weighted regression GWR [ 36 ] or Bayesian spatially varying coefficient process SVCP models [ 35 ] to estimate how alcohol outlet density influences violent crime across local regional areas. In contrast to the spatial regression models above, spatially varying coefficient models do not assume the relationship between alcohol access and crime is constant across space and instead estimate coefficients for regions across the study area e.

In the Bayesian spatial varying coefficient model, random effects intercept and effect parameters are defined in the prior and borrow strength from local data exhibiting spatial autocorrelation defined using contiguity matrix or distance weighted function. The spatially varying coefficient process then uses a prior joint specification of the coefficients that models the spatial correlation of the coefficients as a continuous process i.

To ensure cross-sectional and temporal differences did not bias results, researchers applied either space-time fixed [ 47 , , ] or random [ 25 , 57 , 58 , 85 ] effects for units and time periods. In the fixed effects models, researchers considered the lagged effects of alcohol access or socio-demographics over time [ , ] or space [ 47 ] on the incidence of crime, but did not explore space-time interaction.

In a more complex panel model, Poisson Bayesian space-time misalignment analysis was conducted to estimate how alcohol outlet density in focal region and neighbouring zip codes lag effected the count of assault injuries over 14 years [ 31 ]. The Bayesian spatial misalignment model addressed how the geographic delineation of zip codes varied over the study period. A random county and country level effect were also used to control for the nested structure of the zip codes, and year specific intercepts where implemented to assess statewide changes in assault risk not explained by the neighborhood demographics, alcohol outlet densities, overall hospitalization rates, population density, retail clutter, presence of highways, and ZIP code instability misalignment covariates.

Successive models were run to explore additional lags and bar interactions effects on crime. In two cases, fixed effects were used to model the influence space and time units on crime [ 23 , 46 ] though both studies explored temporally lagged influences on crime including: alcohol consumption per capita [ 23 ] and change in municipal dry laws [ 46 ].

Finally, dummy variables were used to signify if a significant shift in the rate of crime occurred after an alcohol tax change [ 23 ] or restricted alcohol outlet closing times [ 46 ]. The probability of a crash was estimated using previous quarterly state-rate of crashes, the yearly change in crash rate, socio-demographic controls and a random intercept indicating the change in Sunday sales of alcohol zero before, mean sales after sales ban. Weakly informative priors were specified for each parameter in the model leaving the posterior inferences largely influenced by the dataset.

A CAR model was used to monitor changes in assaultive violence after outlet licence surrender assuming a Poisson distribution for crime data. Alcohol exposure was measured as a dichotomous indicator of census tracts surrendering alcohol licenses, the percent of surrender, alcohol outlet density, and a dual change point interaction term specifying the year and tract.

Control covariates included yearly: race, young male population, poverty, and damage per square mile, and a spatial error. The spatial error model accounted for residual similarities across neighbourhoods specifying the prior mean of the error in the focal tract should be equal to the average error in the adjacent census tracts gamma hyperprior distribution having mean 1 and variance 10 used. All other covariates priors were specified as having a normal distribution centered at 0 with precision 0.

Regression trees are a computationally intensive, non-parametric method, of recursively splitting data based on thresholds of the singular variables to maximize the homogeneity within the resulting response groups e. The resulting tree shows a hierarchy of selected explanatory variables, and interactions among, though no formal coefficient estimation or significance testing are available [ ]. To avoid over fitting and provide a more rigorous evaluation of explanatory variables influence on the model fit, bagging and boosting regression trees ensemble methods were developed.

These methods use multiple trees, derived from sub-samples or residual data to predict the response crime to stabilize model results [ ]. Yu et al. Space-time mapping was conducted to understand how liquor violations, assaults, batteries, vandalism, and noise complaints emerged through time and space in proximity to the university bar district of Madison Wisconsin [ ].

Spatial cluster methods illuminated where alcohol outlet densities and crime rates frequencies significantly diverted from an expected random pattern [ ]and cellular automata models were used as the first prospective forecast analysis to assess how relative risk ratios of crime crime as a proportion of alcohol density were expected to disperse with changes in population at risk across a detailed 50m resolution downtown Vancouver British Columbia study [ 48 ]. Alcohol outlet agglomerations were compared to regional violence counts using a foci cluster test specified as the sum of the differences between observed and expected assault counts at each location weighted by the exposure to alcohol outlet agglomeration.

In this sense, the statistic explained a distance decay effect identifying the spatial extent at which the observed number of assaults exceed the expected [ ]. Cellular automata methods, similar to agent based modelling, forecasted crime dispersion based on spatial distribution of alcohol outlet seats using a 50m grid across the Vancouver area. Each grid cell was specified with a number of finite states of possible violent crime risk, and a contiguity neighbourhood around each cell was defined.

The initial state of each cell was trained by observed alcohol outlet seats and violent crime risk. A new state for each cell was created according to a fixed rule blocks with high relative risk were specified to increase violent crime frequency conditional on the current state and of the cells in the adjacent neighbourhood.

The simulation was run times and in each case high risk violent crime blocks multiplied when liquor licenses clustered, creating the first prospective analysis of alcohol exposure and criminal behaviour. A large variety of modelling and exploratory techniques were applied to study the effects of alcohol exposure on criminal behaviour Table 4. Policy makers are interested in how exposure to alcohol affects overall population rates of crime, while also wanting to address neighbour needs for policing around troublesome alcohol establishments, local zoning policy, or approval of new alcohol establishments [ 2 ].

Therefore, estimation and prediction techniques were mindfully selected to provide guidelines for alcohol-crime prevention. We address the strengths and weaknesses of common quantitative approaches, and data collection methods to guide future alcohol-crime research. While it is possible to use ARIMA models for change point analysis, some limitations exist; namely, the removal of temporal trends and seasonal oscillations in crime during the differencing technique to ensure stationarity among the crime series [ 63 ].

Further, the structure of the ARIMA model challenges researchers ability to contend with missing data or explore stochastic exploratory effects on the alcohol-crime relationship [ ]. However, there were drawbacks when considering the statistical assumption of: independence between crime measures, correct specification of link and variance functions, little to no multi-collinearity among the explanatory variables, and independent uncorrelated residuals.

Ignoring implication of time can cause positive serial autocorrelation in errors, and miss any time-lagged effects of the alcohol exposure on crime [ ]. Notably, when serial autocorrelation exists between the temporal units the significance of the intervention variable can be overestimated.

Intervention time-series analysis may be better addressed by mixed modelling approaches incorporating time lagged explanatory variables or structured time series methods that explicitly address trends and seasonality inherent in crime data. Data dependence positive correlation between units can lead to correlated residuals, ultimately reducing the standard error and biasing coefficients [ 38 , ].

More recent publications published since tested for residual spatial autocorrelation [ 10 , 45 , 75 — 77 ] though half did not address the independence assumption. When positive autocorrelation was found, one study remedied significant spatial autocorrelation by removing spatial units instead of applying a more appropriate spatial lag or error model See Section 3.

Without specification of the hierarchies e. The models also become vulnerable to over fitting as the space and time effects are not generalizable to other regions and time periods. Understanding intra space-time patterns is key for alcohol policy planning in an effect to address effects on study applied a jackknifing approach to monitor the impact on the estimated coefficient when one space-time period is left out of the analysis [ 8 ]. Researchers would further benefit from the specification of random space time effects, especially with shorter time-periods and a greater amount of spatial units, in order to conserve statistical power [ ].

Panel models should also consider the implications of alcohol access in previous units and regions as well as within unit variance. Hierarchical models e. Specifically random effects modelling permitted the influence of explanatory variables to fluctuate over space and time random slope or intercept model and can be keenly useful when addressing spatial variation in the expected outcome [ ].

For example, you can condition the estimated value of crime toward the mean for regions with fewer persons instead of predicting extremely low numbers [ , ], particularly useful for small scale regional modelling e. Further, hierarchical models can estimate the effects of explanatory variables on crime measured at multiple scales allowing researchers to consider direct factors e. Mixed modelling also offer approaches for modelling autoregressive processes lagged or spatial error models when the space and time detail in data increase such that researchers have to consider the effects of alcohol access in previous time periods or neighbouring units on the incidence of crime.

Alcohol consumption in one neighbourhood can lead to crime in an adjacent or further region and changes in alcohol policy may have a delayed influence on crime incidence as the population recognizes modifications, increasing the importance of considering lagged variables. Bayesian estimation also provided flexible inference methods for modelling hierarchies [ 32 , 84 ] space [ 31 , 35 ], and space-time [ 30 , 85 , 86 ] dynamics. Improving upon frequentist techniques, Bayesian Spatially Varying Coefficient Process offer inference possibilities for modelling non-stationary datasets controlling for correlation among regionally estimated regression coefficients , in contrast to GWR models which use an iterative algorithm lacking formal statistical properties of inference [ ].

Because of these advantageous we are seeing a recent trend in the publication of Bayesian inference across the alcohol-crime literature seven published since most likely influenced by the increasing hierarchical and space-time detail of data and free software e. In addition to mixed modelling techniques, we also see utility in the less common applied exploratory methods, specifically cluster detection and density mapping, which can illuminate specific risk locations of alcohol-related crime [ ]. Cellular automata also poses an alternative prospective modelling approach where known information about alcohol exposure and crime can train a computation model to predict where crime will lead in future scenarios of exposure [ 48 ].

However, these methods lack tradition coefficient estimation, statistical significance testing, and limit the ability to study simultaneous effects on crime. Parameters are often specified by the user e. What they do provide is local specification of high risk areas for policing and regional planning, and unique methods for predictive simulations when alcohol exposure increases e. Pursuant to modelling considerations we found the practice of standardizing crime counts by residential population data predominant across rate calculations.

It is likely when using smaller geographic units blocks or neighbourhood for analysis the residential population is unrepresentative of population at-risk [ 43 ] displacing the true spatial pattern of crime [ ] thereby altering model results for small areas studies. For example, people living in an area are not necessarily the population consuming alcohol and committing crime.

Often establishments that sell alcohol draw people from neighbouring regions to their premises altering the population at risk in time and space [ ]. Depending on the study, using residential population counts can skew the relative risk scenario of crime and alter relationships estimated in models applying residential population rates, especially across smaller areas such as blocks, census tract, or neighbourhoods where persons could readily venture between. Opportunities exist to use ambient population data data representing the spatial and temporal fluctuations of populations.

Quantitative approaches in climate change ecology

Landscan data redistributes residential population counts, using complex land use models, to identify where persons are mostly likely to spend their time in a 24hr period. Whereas, social media demographic estimates pin media users to the geographic location in time showing demographic variances across space and time, and are likely to represent the younger drinking population vulnerable to nuisance and assault crimes [ 2 , , ]. Generally, we found studies exploring direct alcohol consumption indicators blood alcohol level and consumption patterns identified positive significant results between alcohol consumption and crime [ 6 , 13 , 23 , 29 , 44 , 54 , 55 , 78 , 79 ].

Whereas studies using alcohol exposure measures such as alcohol sales lock-outs [ 18 , 65 ], change in the hours of sales [ 62 , 66 — 69 ], change in establishment hours [ ], modification of alcohol tax [ 60 , 61 , 82 , ] or alcohol outlets measured at the municipal level [ 89 , 91 ] found no significant relationships.

Overall the choice of scale is limited to available data and we can not make conclusions across scales, though improvements can be made to alcohol exposure measures. Simply the difference in measurement of alcohol outlet density per region is one example. Regions of equal outlets and populations can have vastly different access if spread across difference sized areas. Similarly standardizing by area does not represent the paths people readily use for travel. Further, many studies combine alcohol establishment types to model the association between crime and indicators of consumption [ 6 , 8 , 29 , 35 , 90 — 92 , 95 , ].

However, it has been established that specific establishments types contribute disproportionately to increasing the rates of crime [ , ]. To illuminate these connections researchers need disaggregate alcohol establishments, especially across small unit studies were correlation among densities is less likely. Additionally, researchers could explore attributing density measures with seating capacities as not to treat each establishment as having an equal weight on consumption patterns [ 48 ].

Only one study represented on-premises alcohol outlet density using seats [ 48 ]. We recognize the limitations surrounding the level of spatial and temporal detail available for crime models using traditional data sources, such as aggregated police data or government records. The information content provided by social media is being utilized in health research [ ], and could prove resources for crime and alcohol studies.

Participatory mapping, where respondents connect responses in space and time on a geographic interface, could also become a more common application across the consumption and crime surveys to source information about the probable locations of alcohol consumption and witnessed alcohol-attributable crime. The advantages of participatory data collection for health research are well known [ , ], but have not extended to crime-alcohol modelling.

These studies are well poised to draw hierarchical connections between individuals and environmental influences on drinking patterns and subsequent criminal behaviour. Studies connecting consumption to specific locations are invaluable crime prevention, but scarce across the literature. Rarely in these studies are the effects explored outside of the adjacent areas e. To date, explicitly addressing the concept of proximity between alcohol establishments and crime is limited [ 20 , ].

With advances in technology for mapping alcohol establishment and crimes, it is possible to address the diffusion of crime around each establishment in space and time. Using distance decay functions [ — ], parameters can be quantified to explain the expected frequency of crime as a function of distance by treating alcohol establishment locations or clusters as the origins of crime.

Space-time bivariate point pattern analysis [ ] can also statistically assess the spatial extent i. These results would provide evidence based information for setting restrictions on the proximity of alcohol establishments in an area. Mapping has been largely overlooked analysis strategy, likely because of the privacy concerns associated with crime data. However, maps can illuminate data outliers and applicable spatial scales for model assessment. Criminologists to date have had a vested interest in understanding the frequency of crime through space and time and studies have been conducted to address the stability of crime hot-spots [ , ].

In the cases where alcohol establishment densities remain static, it is still useful to study how crime hot spots emerge through hours of the day around these establishments. To observe how clusters of crime form over time three dimensional kernel density mapping [ ], or scan statistics [ ] are possible approaches, providing a novel and interesting perspective for alcohol policy literature. Identifying thresholds at which alcohol access substantively increases crime rates is also an interesting avenue of future studies.

Both Livingston [ 11 ] and McKinney et al. These findings signify a change in the environment, merging from community areas to entertainment districts. To understand if these thresholds are cross-regionally or cross-culturally stable, it is of interest for criminologist and health researchers to employ modelling techniques that can accommodate non-linear response relationships, either in the form of transformed specification before modelling i.

Study designs and statistical approaches characterizing the relationship between crime and alcohol are best chosen based on the research question and nature of data. Researchers studying the influence of alcohol exposures on the rate or count of crime over large areas using multiple spatial units census tracts, neighbourhoods, blocks will likely turn to spatial regression, hierarchical models, and spatial varying coefficient models to capture spatial effects. While, crime data collected over areas considered to be demographically homogenous will mostly likely apply time-series analysis to understand how alcohol policy affects crime over larger population groups.

Novel sources of spatial data are going to create further opportunity to utilize non-traditional methods to study how the size and capacity of drinking establishments impacts consumption and ultimately crime, across space and through time. There are new techniques available for rate calculations across small analysis units, and we anticipate a surge in the spatio-temporal analysis of the alcohol consumption and crime connection. There is a need to inform policing and alcohol policy by identifying how consumption in specific locations influences regional crime.

With advances in spatial-temporal data collection we expect a continued uptake of flexible Bayesian inference, greater inclusion of spatio-temporal point pattern analysis, and prospective modelling over small areas. We would like to thank Dr. Eleanor Setton from the University of Victoria Spatial Science Research Laboratory, and three anonymous reviewers for their helpful comments and suggestions.

National Center for Biotechnology Information , U. PLoS One. Published online Sep Jessica L. Trisalyn A. Keitaro Matsuo, Editor. Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist. Received Aug 28; Accepted Sep This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

This article has been cited by other articles in PMC. Associated Data Data Availability Statement Our article is a review of statistical methods used from various studies which are listed in our reference section. Abstract Modelling the relationship between alcohol consumption and crime generates new knowledge for crime prevention strategies. Introduction Alcohol supply restrictions continue to relax across the globe, leading to increases in disease [ 1 , 2 ], dependency [ 3 ], injury [ 4 , 5 ], and crime [ 6 — 11 ].

Study Selection and Synthesis We searched the alcohol-crime literature from to January using the Web of Science and Google Scholar databases. Table 1 Search term descriptions. Open in a separate window. Fig 1. Results 3. Table 2 Country study areas. Table 3 Applied analysis units counted by country, overall use before and after , and the percent change in use after Percent change in use was calculated by subtracting the proportion of studies applying the analysis unit before from the proportion of studies applying the same unit after Discussion 4.

Table 4 Applied quantitative methods. Most often used to understand if the rate or count of crime changed after an alcohol policy intervention.