Once we have our data, as in all data-driven studies, a key next step is to begin to examine the data. Much like when we run simple frequencies or cross-tabs to explore other forms of data, we do the same general approach with spatiotemporal data.

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In addition to descriptive data analyses, we can examine our data using simple descriptive maps. By doing this, we can get a clear visualization of important characteristics or trends that may be linked to spatial data that we may not see by just looking at the data. We can also pinpoint outliers, potentially erroneous data, and small or large cell counts that may become problematic.

Map A: Breast cancer mortality rates were mapped using clear colors, to see that there may be some clustering around states with lowest rates green and highest rates red. A histogram of rates was also produced to see potential outliers and there is one state Mississippi with higher rates than other states 28 deaths per , Given the findings, you would check to see if these rates are consistent with other years and in other states. Map B: In this map we are using mortality counts to look at potential small cell counts or erroneous data that may cause issues.

We have one large outlier, but further analysis indicates that the state is California, which has a very large population to begin with so it may be less of a concern. The map indicates that there are many small counts in areas with non-concentrated population i.

You may also want to look further into figuring out why — are these low counts because of the low population or is it something else like a data collection issue. Why are these two clusters here? Spatiotemporal data may often need to be transformed before analyzing.

- The Spatial Language of Time: Metaphor, metonymy, and frames of reference.
- The Forbidden Religion.
- Opportunities in Engineering Careers, Rev. Ed. (Opportunities in…Series)!
- Spatio-temporal Approaches: Geographic Objects and Change Process;
- Spatio-temporal Approaches - ISTE;
- Victory in the Wilderness: Growing Strong in Dry Times;

If necessary, use techniques to center the data and use transformations to make the data fit closely to a normal distribution. Another key aspect is to test for non-independence of spatially linked observations. Need to be concerned about clustering, and depending on what your data looks like and what clustering you are expecting, you use different methods. Various ways clustering can occur are :.

If clustering is found you may need to transform data using algorithms which extract potential statistical clusters. Often in spatiotemporal data an issue that may lead to bias is the existence of autocorrelation. This stems back to the requirement we discussed earlier of the analytical models that all spatial objects are independent of each other and all temporal data is independent of it. Autocorrelation is the mechanism through which subjects living closer together may be more similar than expected giving a truly random spatial distribution.

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Or, based on our example of breast cancer mortality rates in the US, states closer to each other may be more similar than states that are further away from each other. In comparison to a traditional correlation, which looks at the relationship between two variables, autocorrelation measures the correlation between a variable X, and the average value of X for neighboring states countries, zip codes, people.

If autocorrelation is due to unmeasured factors that are spatially correlated with your variables of interest, it will introduce bias to the results of the analysis. The presence of autocorrelation violates the independence assumption and your resulting models may have unstable parameter estimates and unreliable p-values for any regression analyses. The most frequently used method to assess autocorrelation was Morans I value. It is the most general calculation as you can use point data or polygons like states , and you can also include all data types, whether you have categorical, binary, or continuous variables, so it may be a good start when assessing your data.

There are many models that are housed within the spatiotemporal framework and that can be used for these types of analyses. It best accounts for local effects, so if you expect to see a lot of within spatial variability differences across individuals this may be an effective method. Not only does the outcome depend on its previous values over time, but also its previous values in space. Often used for data with large distances between space and time points and very large datasets. Takes into consideration APC effects as well as differential geographical effects on behavior.

Often used in cancer models to assess relationships of where people live, how that effects their behavior, in addition to classic APC effects we see in cancer. Provides smoothed parameter estimates along space and time on a large, global scale. The smoothing is carried out in three dimensions longitude, latitude, and time. This can be useful if you expect significant changes at different time points. For example, this method can be used if you wanted to see the effects of health care on a disease outcome across states before and after Affordable Health Care Act.

The temporal distribution of the residuals is explored by means of the time graph display and the spatial distribution by means of the map display. A model is considered correctly generated or captures the general features of spatiotemporal variation when there is an absence of clear temporal and spatial patterns, or in other words, the distributions for each dimension appear as random noise.

If random distribution is not established the analyst may choose to modify the model or segment the group and revise the analysis.

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Other key factors to consider in the evaluation step is to look at the key assumptions of the theoretical ST model — all temporal structures should be captured by the smooth temporal basis function and the spatial dependencies should demonstrate stationarity. Once the model has been satisfactorily built, adjusted and output checked, the results can be used in risk analyses and decision-making. Interpretation of the results depends on whether the model is built to describe novel patterns in health mapping or whether the model was developed to predict future disease outcome patterns.

Since we only described general steps taken to develop a spatiotemporal model for descriptive cases, an example of how results are interpreted can be examined in a study looking at the Age-Specific Spatiotemporal Patterns of Female Breast Cancer Mortality in Spain from — See references. The rapid growth of spatiotemporal datasets due to widespread collection of network and location-aware decides has raised the demand in spatiotemporal data analytic approaches.

These huge collections of spatiotemporal data often hide possibly interesting information and valuable knowledge. Meliker, J. Spatio-temporal epidemiology: principles and opportunities. Spatial and Spatio-Temporal Epidemiology, 2 1 , 1—9. Review paper discussing the basic concepts and utilization of spatio-temporal analysis in epidemiology. Nobre F.

Roddick, J. Basic introduction to spatio-temporal analysis and data mining along with an extensive list of resources and journal articles referring to the topic. Andrienko, N. A visual analytics framework for spatio-temporal analysis and modelling. Data Mining and Knowledge Discovery. Combines traditional spatio-temporal analyses with visual techniques to analyze spatially referenced time series data.

Discusses model selection, adjustment of model parameters, and model evaluation. Chen, Q. Spatio-temporal ecological models. Ecological Informatics, 6 1 , 37— Introduction of a systems dynamic model to address spatio-temporal changes in a population. Fang, X. Additive models with spatio-temporal data. Environmental and Ecological Statistics, 22 1 , 61— Proposes a new approach to using additive models AM with correlated data, particularly spatio-temporal data, based on a penalized likelihood method. Also discusses methods of model selection criteria in data with and without spatial correlation using an example data analysis.

Joon Y. Kamarianakis, Y. Spatial-time series modeling: A review of the proposed methodologies. Law, J. Developed a method to apply Bayesian spatio-temporal modeling to crime trend analysis, particularly in a small-area level. Discusses past methods used to date and benefits of the Bayesian model. MacNab, Y. Spatio-temporal modelling of rates for the construction of disease maps.

Statistics in Medicine, 21 3 , — Focuses on numerous methods behind disease mapping with focus on disease incidence and mortality over both space and time.

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In an example, the article uses generalized additive mixed models to look at infant mortality in Canada over time. Laidre A novel method for identifying behavioural changes in animal movement data Ecology Letters Models are provided for location filtering, location filtering and behavioural state estimation, and their hierarchical versions. The models are primarily intended for fitting to ARGOS satellite tracking data but options exist to fit to other tracking data types. Simplified Markov Chain Monte Carlo convergence diagnostic plotting is provided but users are encouraged to explore tools available in packages such as 'coda' and 'boa'.

It implements the methodology found in the article by Rivest et al.

- Spatio-temporal Approaches: Geographic Objects and Change Process;
- Geographic Process Modeling Based on Geographic Ontology : Open Geosciences;
- The High Window (Philip Marlowe Series, Book 3).
- Geographic Process Modeling Based on Geographic Ontology : Open Geosciences!
- Seeing the Elephant: Understanding Globalization from Trunk to Tail.
- Developments in Polymer Degradation—7;

It also includes a function based on the Lincoln-Petersen Index as applied to radio telemetry data by White and Garrott The model is fit using the Kalman-filter on a state space version of the continuous-time stochastic movement process. As described in Hanks et al.

Miscellaneous functions for handling location data are also provided. Weighted directed graphs have weights from A to B which may differ from those from B to A. Dual-weighted directed graphs have two sets of such weights. A canonical example is a street network to be used for routing in which routes are calculated by weighting distances according to the type of way and mode of transport, yet lengths of routes must be calculated from direct distances. EMbC Unsupervised, multivariate, binary clustering for meaningful annotation of data, taking into account the uncertainty in the data.

A specific constructor for trajectory analysis in movement ecology yields behavioural annotation of trajectories based on estimated local measures of velocity and turning angle, eventually with solar position covariate as a daytime indicator, "Expectation-Maximization Binary Clustering for Behavioural Annotation". The file in question is an assorted collection of messages, events and raw data. This R package will attempt to make sense of it.

Offers several popular types of analyses, including linear and growth curve time analyses, onset-contingent reaction time analyses, as well as several non-parametric bootstrapping approaches. Fish and Fisheries. FLightR Spatio-temporal locations of an animal are computed from annotated data with a hidden Markov model via particle filter algorithm.

The package is relatively robust to varying degrees of shading.