The Modified Temporal Unit Problem (MTUP) is a source of statistical bias that occurs in time series and spatial analysis when using temporal data that has been aggregated into temporal units. [1] [2] In such cases, choosing a temporal unit (e.g., days, months, years) can affect the analysis results and lead to inconsistencies or errors in statistical hypothesis testing. [3]
The MTUP is closely related to the modifiable areal unit problem or MAUP, in that they both relate to the scale of analysis and the issue of choosing an appropriate analysis. [2] [4] While the MAUP refers to the choice of spatial enumeration units, the MTUP arises because different temporal units have different properties and characteristics, such as the number of periods they contain or the amount of detail they provide. [2] [4] [5] For example, daily sales data for a product can be aggregated into weekly, monthly, or yearly sales data. In this case, using monthly data instead of daily data can result in losing important information about the timing of events, and using yearly data can obscure short-term trends and patterns. [3] However, the daily data in the example may have too much noise, temporal autocorrelation, or be inconsistent with other datasets. [1] With only daily data, conducting an analysis accurately at the hourly rate would not be possible. In addition, the Modifiable Temporal Unit Problem can also arise when the time units are irregular or when the data is missing for some periods. In such cases, the choice of the time unit can affect the amount of missing data, which can impact the accuracy of the analysis and forecasting.
Overall, the Modifiable Temporal Unit Problem highlights the importance of carefully considering the time unit when analyzing and forecasting time series data. [1] It is often necessary to try different time units and evaluate the results to determine the most appropriate choice. [1]
Temporal autocorrelation refers to the degree of correlation or similarity between values of a variable at different time points. [6] [7] It examines how a variable's past values are related to its current values over a sequence of time intervals. [6] High temporal autocorrelation implies that past observations influence future observations, while low autocorrelation suggests that current values are independent of past values. This concept is often used in time series analysis to understand patterns, trends, and dependencies within a time-ordered dataset, helping to make predictions and infer the underlying dynamics of a system over time. By adjusting the temporal unit used to bin the data in the analysis, temporal autocorrelation can be addressed. [2]
The impact of MTUP on crime analysis can be significant, as it can affect the accuracy and reliability of crime data and its conclusions about crime patterns and trends. [3] For example, suppose the temporal unit of analysis is changed from days to weeks. In that case, the number of reported crimes may decrease or increase, even if the underlying pattern remains constant. This can lead to incorrect conclusions about the effectiveness of crime prevention strategies or the overall level of crime in a given area. [3]
The MTUP can also have an impact on food accessibility. [4] This issue arises when the temporal unit of analysis is changed, leading to changes in the patterns and trends observed in food accessibility data. For example, if food accessibility data is analyzed from different years or aggregated differently, then the results of a study are likely to be impacted. [4] This can affect our understanding of the availability of food in different areas over time, and can result in incorrect or incomplete conclusions about food accessibility. [4]
The MTUP can affect our understanding of the incidence and prevalence of diseases or health outcomes in different populations over time, resulting in incorrect or incomplete conclusions about the public health situation. [8] [9] The timeframe chosen for collecting and analyzing public health data is something that needs to be considered by researchers. [8]
To address the MTUP, it is important to consider the temporal resolution of the data and choose the most appropriate temporal unit based on the research question and the goals of the analysis. [1] In some cases, it may be necessary to aggregate or interpolate the data to a consistent temporal unit. Additionally, it may be helpful to use multiple temporal units or to present results for different temporal units to demonstrate the sensitivity of the results to the choice of temporal unit. [1]
A choropleth map is a type of statistical thematic map that uses pseudocolor, meaning color corresponding with an aggregate summary of a geographic characteristic within spatial enumeration units, such as population density or per-capita income.
Spatial ecology studies the ultimate distributional or spatial unit occupied by a species. In a particular habitat shared by several species, each of the species is usually confined to its own microhabitat or spatial niche because two species in the same general territory cannot usually occupy the same ecological niche for any significant length of time.
The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." This first law is the foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method for spatial interpolation and to support the regionalized variable theory for kriging. The first law of geography is the fundamental assumption used in all spatial analysis.
Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data. It may also be applied to genomics, as in transcriptomics data.
The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. MAUP affects results when point-based measures of spatial phenomena are aggregated into spatial partitions or areal units as in, for example, population density or illness rates. The resulting summary values are influenced by both the shape and scale of the aggregation unit.
Spatial epidemiology is a subfield of epidemiology focused on the study of the spatial distribution of health outcomes; it is closely related to health geography.
A thematic map is a type of map that portrays the geographic pattern of a particular subject matter (theme) in a geographic area. This usually involves the use of map symbols to visualize selected properties of geographic features that are not naturally visible, such as temperature, language, or population. In this, they contrast with general reference maps, which focus on the location of a diverse set of physical features, such as rivers, roads, and buildings. Alternative names have been suggested for this class, such as special-subject or special-purpose maps, statistical maps, or distribution maps, but these have generally fallen out of common usage. Thematic mapping is closely allied with the field of Geovisualization.
In the context of spatial analysis, geographic information systems, and geographic information science, a field is a property that fills space, and varies over space, such as temperature or density. This use of the term has been adopted from physics and mathematics, due to their similarity to physical fields (vector or scalar) such as the electromagnetic field or gravitational field. Synonymous terms include spatially dependent variable (geostatistics), statistical surface ( thematic mapping), and intensive property (physics and chemistry) and crossbreeding between these disciplines is common. The simplest formal model for a field is the function, which yields a single value given a point in space (i.e., t = f(x, y, z) )
Statistical geography is the study and practice of collecting, analysing and presenting data that has a geographic or areal dimension, such as census or demographics data. It uses techniques from spatial analysis, but also encompasses geographical activities such as the defining and naming of geographical regions for statistical purposes. For example, for the purposes of statistical geography, the Australian Bureau of Statistics uses the Australian Standard Geographical Classification, a hierarchical regionalisation that divides Australia up into states and territories, then statistical divisions, statistical subdivisions, statistical local areas, and finally census collection districts.
Geographic information systems (GISs) and geographic information science (GIScience) combine computer-mapping capabilities with additional database management and data analysis tools. Commercial GIS systems are very powerful and have touched many applications and industries, including environmental science, urban planning, agricultural applications, and others.
A dot distribution map is a type of thematic map that uses a point symbol to visualize the geographic distribution of a large number of related phenomena. Dot maps are a type of unit visualizations that rely on a visual scatter to show spatial patterns, especially variances in density. The dots may represent the actual locations of individual phenomena, or be randomly placed in aggregation districts to represent a number of individuals. Although these two procedures, and their underlying models, are very different, the general effect is the same.
A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with areal data, statistics should be interpreted based upon the boundary.
A spatial distribution in statistics is the arrangement of a phenomenon across the Earth's surface and a graphical display of such an arrangement is an important tool in geographical and environmental statistics. A graphical display of a spatial distribution may summarize raw data directly or may reflect the outcome of a more sophisticated data analysis. Many different aspects of a phenomenon can be shown in a single graphical display by using a suitable choice of different colours to represent differences.
Spatial econometrics is the field where spatial analysis and econometrics intersect. The term “spatial econometrics” was introduced for the first time by the Belgian economist Jean Paelinck in the general address he delivered to the annual meeting of the Dutch Statistical Association in May 1974 . In general, econometrics differs from other branches of statistics in focusing on theoretical models, whose parameters are estimated using regression analysis. Spatial econometrics is a refinement of this, where either the theoretical model involves interactions between different entities, or the data observations are not truly independent. Thus, models incorporating spatial auto-correlation or neighborhood effects can be estimated using spatial econometric methods. Such models are common in regional science, real estate economics, education economics, housing market and many others. Adopting a more general view, in the by-law of the Spatial Econometrics Association, the discipline is defined as the set of “models and theoretical instruments of spatial statistics and spatial data analysis to analyse various economic effects such as externalities, interactions, spatial concentration and many others”. Recent developments tend to include also methods and models from social network econometrics.
In geography, scale is the level at which a geographical phenomenon occurs or is described. This concept is derived from the map scale in cartography. Geographers describe geographical phenomena and differences using different scales. From an epistemological perspective, scale is used to describe how detailed an observation is, while ontologically, scale is inherent in the complex interaction between society and nature.
Isabelle Thomas is a professor of geography at the Université Catholique de Louvain in Belgium and research director of the National Fund for Scientific Research. She is member of the Center for Operations Research and Econometrics (CORE)
The second law of geography, according to Waldo Tobler, is "the phenomenon external to a geographic area of interest affects what goes on inside." This is an extension of his first. He first published it in 1999 in reply to a paper titled "Linear pycnophylactic reallocation comment on a paper by D. Martin" and then again in response to criticism of his first law of geography titled "On the First Law of Geography: A Reply." Much of this criticism was centered on the question of if laws were meaningful in geography or any of the social sciences. In this document, Tobler proposed his second law while recognizing others have proposed other concepts to fill the role of 2nd law. Tobler asserted that this phenomenon is common enough to warrant the title of 2nd law of geography. Unlike Tobler's first law of geography, which is relatively well accepted among geographers, there are a few contenders for the title of the second law of geography. Tobler's second law of geography is less well known but still has profound implications for geography and spatial analysis.
Arbia’s law of geography states, "Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution." Originally proposed as the 2nd law of geography, this is one of several laws competing for that title. Because of this, Arbia's law is sometimes referred to as the second law of geography, or Arbia's second law of geography.
The uncertain geographic context problem or UGCoP is a source of statistical bias that can significantly impact the results of spatial analysis when dealing with aggregate data. The UGCoP is very closely related to the Modifiable areal unit problem (MAUP), and like the MAUP, arises from how we divide the land into areal units. It is caused by the difficulty, or impossibility, of understanding how phenomena under investigation in different enumeration units interact between enumeration units, and outside of a study area over time. It is particularly important to consider the UGCoP within the discipline of time geography, where phenomena under investigation can move between spatial enumeration units during the study period. Examples of research that needs to consider the UGCoP include food access and human mobility.
The neighborhood effect averaging problem or NEAP delves into the challenges associated with understanding the influence of aggregating neighborhood-level phenomena on individuals when mobility-dependent exposures influence the phenomena. The problem confounds the neighbourhood effect, which suggests that a person's neighborhood impacts their individual characteristics, such as health. It relates to the boundary problem, in that delineated neighborhoods used for analysis may not fully account for an individuals activity space if the borders are permeable, and individual mobility crosses the boundaries. The term was first coined by Mei-Po Kwan in the peer-reviewed journal "International Journal of Environmental Research and Public Health" in 2018.