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Using the Specification Curve to Teach Spatial Data Analysis and Explore Geographic Uncertainties

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Title: Using the Specification Curve to Teach Spatial Data Analysis and Explore Geographic Uncertainties
Language: English
Authors: Kedron, Peter (ORCID 0000-0002-1093-3416), Quick, Matthew (ORCID 0000-0002-1112-9323), Hilgendorf, Zach (ORCID 0000-0002-0438-6516), Sachdeva, Mehak (ORCID 0000-0003-4375-5422)
Source: Journal of Geography in Higher Education. 2022 46(2):304-314.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 11
Publication Date: 2022
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Geography Instruction, Data Analysis, Meta Analysis, Decision Making, Computer Software, Instructional Materials, Teaching Methods, Regression (Statistics), Predictor Variables, Visual Aids, Geographic Information Systems, Information Science, Housing, Goodness of Fit, Costs, Ownership, Generalization, Publications, Bias
Geographic Terms: Maryland (Baltimore)
DOI: 10.1080/03098265.2021.1901076
ISSN: 0309-8265
1466-1845
Abstract: Educational materials focused on spatial data analysis often feature mathematical descriptions of methods and step-by-step instructions of software tools, but infrequently discuss the set of decisions involved in specifying a statistical model. Failing to consider model specification may lead to specification searching, or the process of repeating analyses to obtain results that meet the criteria thought to be required for publication, and the disproportionate reporting of false-positive results in the academic literature. This article proposes that the specification curve -- a meta-analytical technique that visualizes the specifications and results from a large set of justifiable and plausible statistical models -- be used as a pedagogical tool to teach (spatial) data analysis and explore the geographic uncertainties that arise when specifying and interpreting spatial regression models. An example specification curve that focuses on two common specification decisions in a spatial regression model, specifically selecting predictor variables and constructing the spatial weight matrix, is illustrated. Strategies for using the specification curve in educational contexts to develop analytical plans, reflect on the generalizability of research findings, and highlight issues of replicability and publication bias are proposed.
Abstractor: As Provided
Entry Date: 2022
Accession Number: EJ1344171
Database: ERIC
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  Value: <anid>AN0156218662;jgh01may.22;2022Apr12.03:45;v2.2.500</anid> <title id="AN0156218662-1">Using the specification curve to teach spatial data analysis and explore geographic uncertainties </title> <p>Educational materials focused on spatial data analysis often feature mathematical descriptions of methods and step-by-step instructions of software tools, but infrequently discuss the set of decisions involved in specifying a statistical model. Failing to consider model specification may lead to specification searching, or the process of repeating analyses to obtain results that meet the criteria thought to be required for publication, and the disproportionate reporting of false-positive results in the academic literature. This article proposes that the specification curve – a meta-analytical technique that visualizes the specifications and results from a large set of justifiable and plausible statistical models – be used as a pedagogical tool to teach (spatial) data analysis and explore the geographic uncertainties that arise when specifying and interpreting spatial regression models. An example specification curve that focuses on two common specification decisions in a spatial regression model, specifically selecting predictor variables and constructing the spatial weight matrix, is illustrated. Strategies for using the specification curve in educational contexts to develop analytical plans, reflect on the generalizability of research findings, and highlight issues of replicability and publication bias are proposed.</p> <p>Keywords: Model specification; spatial analysis; uncertainty; geography education; geographic information science; regression</p> <hd id="AN0156218662-2">Introduction</hd> <p>The collection, analysis, and visualization of spatial data are essential components of spatial literacy and spatial thinking (Jarvis, [<reflink idref="bib28" id="ref1">28</reflink>]; Bednarz & Lee, [<reflink idref="bib7" id="ref2">7</reflink>]; Bednarz & Kemp, [<reflink idref="bib8" id="ref3">8</reflink>]; Wakabayashi & Ishikawa, [<reflink idref="bib44" id="ref4">44</reflink>]), and are the cornerstones of geography curricula in research methods, statistics, Geographic Information Science (GIScience), and spatial analysis courses (Bearman et al., [<reflink idref="bib6" id="ref5">6</reflink>]; Goodchild, [<reflink idref="bib22" id="ref6">22</reflink>]). In these courses, regression modeling is often presented as a method suitable for exploring and testing research hypotheses focused on the relationships between outcome and predictor variables (Dunn, [<reflink idref="bib16" id="ref7">16</reflink>]; Florax & Rey, [<reflink idref="bib17" id="ref8">17</reflink>]; Haining, [<reflink idref="bib24" id="ref9">24</reflink>]). Educational materials focused on regression modeling often feature mathematical descriptions of the technique, detailed discussions of the assumptions required for valid statistical inference, and step-by-step instructions for students to replicate while learning how to implement the technique in a software program (Bennett, [<reflink idref="bib9" id="ref10">9</reflink>]; Gregory, [<reflink idref="bib23" id="ref11">23</reflink>]; Mustafa, [<reflink idref="bib32" id="ref12">32</reflink>]; R. P. Haining, [<reflink idref="bib26" id="ref13">26</reflink>]).</p> <p>Often overlooked in regression-focused instructional materials is model specification. Model specification refers to the set of decisions that lead to a statistical model being developed and implemented. Model specification is an important part of the data analysis process as it links the statistical framework of regression with the domain-specific knowledge and theoretical reasoning that motivates and structures a research question. For example, the specification of a non-spatial regression model involves researchers, data analysts, and/or students selecting and operationalizing outcome and predictor variables, choosing a model likelihood, and developing a set of rules for including/excluding outlier data (Simonsohn et al., [<reflink idref="bib38" id="ref14">38</reflink>]). Additional model specification decisions are required for spatial regression models that account for spatial autocorrelation and/or non-stationarity, such as selecting a type of spatial model (e.g., spatial lag or spatial error), choosing how to measure the geographical interactions between locations, and determining how the intensity of geographical interactions vary according to distance or adjacency (Anselin, [<reflink idref="bib4" id="ref15">4</reflink>]).</p> <p>Despite the importance of model specification, many teaching materials illustrate the practice of specification searching. Specification searching occurs when multiple alternative model specifications are tested, a final is model identified, and the results of the final model are presented as the only set of results. The practice of specification searching may lead to many unintended and problematic consequences. By working to identify and report the results of only a single model, students are (implicitly) taught to discard plausible data analyses, retain the models that produce results consistent with certain statistical criteria (e.g., statistical significance), and modify research questions during the data analysis process to align with the most interesting or most publishable results. Applied broadly to the scientific community, past research has suggested that specification searching leads to the published literature being disproportionately composed of false-positive results and to the absence of studies that do not meet the criteria thought to be required for peer-reviewed publication (Ioannidis, [<reflink idref="bib27" id="ref16">27</reflink>]; Rosenthal, [<reflink idref="bib36" id="ref17">36</reflink>]).</p> <p>This article examines and evaluates the specification curve as a pedagogical tool that can be used to teach spatial data analysis and examine the geographic uncertainties that arise when specifying and interpreting spatial regression models. The specification curve is a meta-analytical technique that is composed of two figures; the first shows key model results (e.g., coefficient estimates for one predictor variable) from a set of regression models and the second displays the model specification that produced each result. Using the specification curve helps to identify a universe of plausible and justifiable statistical models, visualize and compare the results of these models, and investigate if, and how, model assumptions influence research results (Simonsohn et al., [<reflink idref="bib38" id="ref18">38</reflink>]). In the classroom, the specification curve provides an opportunity for instructors and students to develop analytical plans, explore various forms of geographic uncertainty, critically reflect on the generalizability and sensitivity of research results, and highlight issues of replicability and publication bias.</p> <hd id="AN0156218662-3">Model specification in spatial regression learning materials</hd> <p>To understand how existing educational materials present model specification, 12 commonly adopted spatial analysis textbooks (Table 1) and 14 publicly available online spatial regression learning materials were reviewed (Table 2). These materials were identified using an internet keyword search for topics related to spatial regression, spatial statistics, and spatial analysis. The online materials included tutorials and software workbooks, workshop materials, and university course materials. Each resource was assessed for its treatment of model specification for both non-spatial regression models and spatial regression models.</p> <p>Table 1. The treatment of selected aspects of regression model specification in textbooks</p> <p> <ephtml> <table><thead><tr><td /><td>Non-spatial Regression</td><td>Spatial Regression</td></tr><tr><td>Texts</td><td>PS</td><td>PI</td><td>FF</td><td>OM</td><td>MS</td><td>WS</td></tr></thead><tbody><tr><td><italic>Spatial Regression Models</italic> Ward and Gleditsch (<xref ref-type="bibr" rid="bibr45">2018</xref>)</td><td>X</td><td /><td /><td /><td>X</td><td>X</td></tr><tr><td><italic>Spatial Econometrics</italic> Kelejian and Piras (<xref ref-type="bibr" rid="bibr29">2017</xref>)</td><td>X</td><td /><td>X</td><td /><td>X</td><td>X</td></tr><tr><td><italic>Statistical Methods for Geography</italic> Rogerson (<xref ref-type="bibr" rid="bibr34">2015</xref>)</td><td>X</td><td>X</td><td>X</td><td>X</td><td /><td>X</td></tr><tr><td><italic>Introduction to R for Spatial Analysis and Mapping</italic> Brunsdon and Comber (<xref ref-type="bibr" rid="bibr10">2015</xref>)</td><td /><td /><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td><italic>Statistics for Spatial Data</italic> Cressie (<xref ref-type="bibr" rid="bibr14">2015</xref>)</td><td /><td /><td>X</td><td>X</td><td>X</td><td /></tr><tr><td><italic>Modern Spatial Econometrics in Practice</italic> Anselin and Rey (<xref ref-type="bibr" rid="bibr5">2014</xref>)</td><td>X</td><td /><td>X</td><td /><td>X</td><td>X</td></tr><tr><td><italic>Introduction to Spatial Econometrics</italic> LeSage and Pace (<xref ref-type="bibr" rid="bibr30">2009</xref>)</td><td /><td /><td>X</td><td /><td>X</td><td>X</td></tr><tr><td><italic>The Sage Handbook of Spatial Analysis</italic> Fotheringham and Rogerson (<xref ref-type="bibr" rid="bibr19">2008</xref>)</td><td /><td /><td /><td /><td>X</td><td>X</td></tr><tr><td><italic>Geospatial Analysis</italic> deSmith et al. (<xref ref-type="bibr" rid="bibr15">2007</xref>)</td><td /><td /><td>X</td><td /><td>X</td><td /></tr><tr><td><italic>Spatial Data Analysis: Theory and Practice</italic> Haining (<xref ref-type="bibr" rid="bibr25">2003</xref>)</td><td /><td /><td>X</td><td /><td>X</td><td /></tr><tr><td><italic>Spatial Analysis and GIS</italic> Fotheringham and Rogerson (<xref ref-type="bibr" rid="bibr18">1994</xref>)</td><td /><td /><td /><td>X</td><td>X</td><td /></tr><tr><td><italic>Spatial Econometrics Methods and Models</italic> Anselin (<xref ref-type="bibr" rid="bibr1">1988</xref>)</td><td /><td /><td /><td /><td>X</td><td /></tr></tbody></table> </ephtml> </p> <p>Table 2. The treatment of selected aspects of regression model specification in online materials</p> <p> <ephtml> <table><thead><tr><td /><td>Non-spatial Regression</td><td>Spatial Regression</td></tr><tr><td>Online Material</td><td>PS</td><td>PI</td><td>FF</td><td>OM</td><td>MS</td><td>WS</td></tr></thead><tbody><tr><td><bold>Tutorials and Software Workbooks</bold></td><td /><td /><td /><td /><td /><td /></tr><tr><td><italic>Geographic Data Science with PySal – Spatial Regression</italic> Rey and Arribas-Bel (<xref ref-type="bibr" rid="bibr33">2018</xref>)</td><td>X</td><td /><td /><td /><td>X</td><td>X</td></tr><tr><td><italic>GIS & Spatial Econometrics</italic> Burkey (<xref ref-type="bibr" rid="bibr12">2018</xref>)</td><td>X</td><td /><td /><td /><td>X</td><td>X</td></tr><tr><td><italic>Spatial Regression Analysis in R: A Workbook</italic> Anselin (<xref ref-type="bibr" rid="bibr3">2007</xref>)</td><td /><td /><td /><td /><td>X</td><td>X</td></tr><tr><td><italic>Spatial Regression: A Brief Introduction</italic><xref ref-type="bibr" rid="bibr11">Brusilovskiy, No Date</xref></td><td /><td /><td>X</td><td /><td>X</td><td>X</td></tr><tr><td><bold>Workshop Materials</bold></td><td /><td /><td /><td /><td /><td /></tr><tr><td><italic>Applied Spatial Analysis for Public Health</italic> Sturrock & Pacheco (2020)</td><td>X</td><td /><td>X</td><td /><td>X</td><td>X</td></tr><tr><td><italic>Spatial Statistics: Regression</italic> Murack (<xref ref-type="bibr" rid="bibr31">2015</xref>)</td><td /><td /><td /><td>X</td><td>X</td><td /></tr><tr><td><italic>Spatial Regression Modeling</italic> Voss and Curtis (<xref ref-type="bibr" rid="bibr42">2011</xref>)</td><td /><td /><td /><td /><td>X</td><td /></tr><tr><td><bold>University Course Materials</bold></td><td /><td /><td /><td /><td /><td /></tr><tr><td><italic>Notebook on Spatial Data Analysis</italic> Smith (<xref ref-type="bibr" rid="bibr39">2020</xref>)</td><td /><td /><td>X</td><td /><td>X</td><td>X</td></tr><tr><td><italic>Spatial Analysis and Regression</italic> Spielman (<xref ref-type="bibr" rid="bibr40">2015</xref>)</td><td>X</td><td /><td>X</td><td /><td>X</td><td>X</td></tr></tbody></table> </ephtml> </p> <p>1 Notes: Hyperlinks to the online materials are provided in the references</p> <p>For non-spatial regression models, we emphasized predictor selection (PS), predictor interactions (PI), functional form (FF), and outlier management (OM) (Simonsohn et al., [<reflink idref="bib38" id="ref19">38</reflink>]). FF broadly refers to the decisions that alter interpretation of the regression results, such as the model likelihood and the transformation of variables. Focusing on the most common spatial regression techniques (spatial lag, spatial error, and geographically weighted regression), we considered PS, PI, FF, and OM, as well as discussions of model selection (MS) and weight selection (WS). MS refers to how alternative spatial regression model types are compared and WS refers to how the spatial interactions between location pairs are measured and specified.</p> <p>While all of the textbooks included material on some aspect of model specification, only four covered the majority of specification decisions; as such, a collected, focused, and in-depth discussion of model specification was not observed in these materials (Table 1). Of the conventional regression topics, FF was the most frequently covered (8 texts), PS was included in the about one-third of the resources (4 texts), and PI received limited treatment (1 text). The spatial regression texts provided more comprehensive reviews of MS (11 texts) and WS (7 texts) as both decisions are essential for specifying a spatial model. In general, model specification was framed as a series of steps completed during the construction of a single final model; Rogerson's ([<reflink idref="bib34" id="ref20">34</reflink>]) treatment of the topics is representative, where the assumptions and decisions involved in regression analysis are discussed but presented separately from content related to spatial modeling. Integrating model specification and spatial regression, Anselin's chapter in the Sage Handbook of Spatial Analysis (2009) offers an in-depth discussion of MS (via likelihood tests) and reviews how spatial models improve upon conventional non-spatial models, and Brunsdon and Comber ([<reflink idref="bib10" id="ref21">10</reflink>]) thoroughly examine WS and provide hands-on examples to illustrate key aspects of this decision.</p> <p>Like the textbooks, the online learning materials reviewed in this article primarily focus on teaching the statistical fundamentals of spatial regression models and the steps required to implement this technique. The balance between fundamentals and implementation varied with the type and purpose of the material. For example, the materials designed to introduce specific software (Anselin, [<reflink idref="bib3" id="ref22">3</reflink>]; Rey & Arribas-Bel, [<reflink idref="bib33" id="ref23">33</reflink>]; Sturrock & Pacheco, [<reflink idref="bib41" id="ref24">41</reflink>]) discuss specification decisions independently and link these decisions together via diagnostic tests often produced by the software. This is illustrated by the workbook that accompanies the GeoDa software (Anselin, [<reflink idref="bib3" id="ref25">3</reflink>]), which emphasizes MS via likelihood ratio tests but does not link this specification decision to other elements, such as WS or PI. (Note that a more comprehensive presentation of specification is included in the lecture series featured on the GeoDa website.) The tutorial and workshop materials (Burkey, [<reflink idref="bib12" id="ref26">12</reflink>]; Voss & Curtis, [<reflink idref="bib42" id="ref27">42</reflink>]) offer a more in-depth discussion of selected aspects of the specification process. For example, Burkey ([<reflink idref="bib12" id="ref28">12</reflink>]) provide an extensive discussion of seven alternative spatial models and a careful treatment of both the conceptualization and specification of WS.</p> <p>The instructional content that accompanies university coursework provided the most comprehensive coverage of model specification. For example, the lecture materials provided by Spielman ([<reflink idref="bib40" id="ref29">40</reflink>]) offer a detailed treatment of both MS and WS that includes foundational discussions of these decision and simulation results that illustrate their impact on regression outputs. Smith ([<reflink idref="bib39" id="ref30">39</reflink>]) similarly offers a comprehensive notebook that builds up the intuition and statistical theorems that motivate the MS and WS decisions and alternative FFs. Collectively, the materials reviewed address all aspects of regression specification, but do not present a comprehensive or integrated discussion of model specification or how model specification can be used to identify and explore a universe of plausible, justifiable, and statistically valid models.</p> <hd id="AN0156218662-4">A specification curve analysis of home prices in Baltimore</hd> <p>Before discussing how the specification curve can be used in geography pedagogy, it is first instructive to understand how specification curves are constructed as well as some of the specification decisions involved in spatial regression modeling. The specification curve illustrated in this article uses a dataset of 211 home prices in Baltimore, Maryland, and investigates the association between dwelling age and dwelling price, controlling for a series of covariates (e.g., home age, size).[<reflink idref="bib1" id="ref31">1</reflink>] Without considering the processes involved in formulating a research question and collecting suitable data, constructing a specification curve involves three steps, as described below.</p> <hd id="AN0156218662-5">Step 1: Identify fixed and flexible model components</hd> <p>The researcher, analyst, or student must first identify the fixed model components that are critical to the research question and the flexible model components that can be modified to represent a range of plausible data-generating processes. In this example, the fixed components were the model likelihood (Gaussian) and the inclusion of dwelling age as a predictor variable. Because it is possible to construct a specification curve for each predictor variable included in a given analysis, researchers should consider focusing specifically on the predictor variable(s) that are the focus of the research question (i.e., the coefficients that support or reject research hypotheses after adjusting for known risk factors). The flexible components were the model type (non-spatial and spatial; D<subs>1</subs> = 2 in Figure 1), the inclusion of additional predictor variables, and the spatial weight matrix specification.</p> <p>Graph: Figure 1. Model specification flowchart for the case study. The model specification decisions are denoted as D and the subscripts indicate the order of the decision. The quantity associated with each decision indicates the number of specifications considered. The total number of models is indicated by M.</p> <hd id="AN0156218662-6">Step 2: Identify alternative specifications for flexible components</hd> <p>After identifying the fixed and flexible model components, the researcher, analyst, or student must consider the range of plausible specifications for each flexible component. In this example, two model types were tested – non-spatial ordinary least squares regression and spatial error regression – and both model types explored five specifications for the set of predictor variables (age, size, structural characteristics, amenities, and location). For the spatial error regression model, two additional flexible components were considered: the form of spatial interactions between locations (queen or rook contiguity, distance-based, or nearest neighbor) and the intensity of spatial interactions (i.e., numerical values included in the weight matrix: binary, distance, inverse-weighted distance). For the purposes of this example, we restricted the spatial regression models to a spatial error model (D<subs>2</subs> = 1), three types of spatial weights (D<subs>3</subs> = 3), twenty-one spatial weight parameterizations (D<subs>4</subs> = 21), and five sets of explanatory variables (D<subs>5</subs> = 5). This resulted in a total of 110 plausible models; five were non-spatial regression models and 105 were spatial error regression models (<emph>M</emph> in Figure 1). In practice, there are many more forms of geographic uncertainty to be examined that would dramatically increase the number of plausible models.</p> <hd id="AN0156218662-7">Step 3: Fit models and construct specification curve</hd> <p>The third step is to fit the universe of plausible models and visualize the results on a specification curve. For this case study, Figure 2 visualizes the specification curve showing the results of the dwelling age coefficient. This specification curve shows that the association between dwelling age and dwelling price is negative across all of the model specifications but statistically significant (at p < 0.05) in only half of the models (52 of 105). Visualizing the results using a specification curve also illustrates that many of the coefficients identified to be statistically significant under some specifications were virtually identical in sign, magnitude, and uncertainty to those identified as non-significant. For example, the associations between dwelling price and dwelling age in Models 49 (β = −14.63), 50 (β = −14.63), and 51 (β = −14.63) were found to be statistically insignificant (at p < 0.05) yet had nearly the exact same coefficient magnitude and uncertainty bounds as the statistically significant result identified in Model 52 (β = −14.45).</p> <p>PHOTO (COLOR): Figure 2. A specification curve for the regression coefficient quantifying the association between dwelling age and dwelling price. The model specifications are ranked from small to large coefficient magnitudes (left to right). The top plot shows the point estimates and 95% CIs of the regression coefficients, the middle plot shows the AIC values for each model, and the bottom plot lists the set of analytical decisions on the left and the specifications of each model with vertical dashes. Statistically significant estimates (p < 0.05) are shown in red and insignificant estimates (p > 0.05) are shown in black. The dashed horizontal line on the top plot indicates the AIC-weighted coefficient estimate (see below).</p> <hd id="AN0156218662-8">Using the specification curve as a pedagogical tool</hd> <p>Complementing mathematical descriptions of regression and step-by-step software instructions, the specification curve provides an opportunity for instructors and students to develop analytical plans that explore various forms of geographic uncertainty, critically reflect on the generalizability and sensitivity of research findings, and highlight issues of reproducibility and publication bias. Focusing first on the development of analytical plans, the specification curve provides a framework for students to identify the fixed and flexible components of a research question, consider the many decisions involved in a data analysis, and identify a range of plausible model specifications. In the classroom, instructors and students can create analytical plans by outlining a set of models to be examined; debating model specifications based on the motivating theories, research hypotheses, and the existing evidence; testing the models individually or in small groups; and collectively summarizing the results using a specification curve. This framework supports existing pedagogical research suggesting that graphical, iterative, and interactive approaches to teaching spatial data analysis facilitate deeper engagement with key concepts (Dunn, [<reflink idref="bib16" id="ref32">16</reflink>]).</p> <p>For spatial regression models, in particular, specification debates should focus on the decisions involving geographic uncertainties, such as the spatial model type, spatial weight type, and spatial weight parameterization (see Figure 1), as these decisions are necessarily made with incomplete knowledge regarding the spatial structure of geographic phenomena. Of particular importance is the interpretation of coefficients in spatial regression models. In this paper, we restrict our analysis to ordinary least squares and spatial error model regression models because the coefficients in both of these model types can be interpreted as the marginal effect of the predictor variable on the conditional mean of the outcome. However, the coefficient estimates of other common spatial regression models cannot be interpreted in this way (see LeSage & Pace, [<reflink idref="bib30" id="ref33">30</reflink>]); in spatial lag regression model, for example, the coefficients represent the combination of the direct effects, which are analogous to the marginal effects discussed above, and the indirect effects, which are the product of spatial spillovers. Specification curves that include spatial lag models should include only the direct effect estimates to ensure that comparisons are consistent and meaningful.</p> <p>The specification curve also provides an opportunity for instructors to interrogate the sensitivity and generalizability of research findings to model specification. In this case study, for example, the specification curve shows that the statistical significance of coefficients is sensitive to model specification and that model interpretations based on thresholds of statistical significance provide do not align with model interpretations focused on coefficient magnitude or practical importance (i.e., two models can produce virtually identical coefficient estimates but only one model produces a significant result at p < 0.05) (Gelman & Stern, [<reflink idref="bib21" id="ref34">21</reflink>]). These issues would be overlooked if researchers, data analysts, or students engaged in specification searching and reported the results of only one model.</p> <p>Additionally, the specification curve can be used in lessons focused on the generalizability of research to alternative plausible and justifiable model specifications. For example, following discussions of the ways in which spatial data analyses can be justified, interpreted, and reported, the specification curve can be used to introduce model averaging, which combines the results of multiple data analyses into a single overall quantity of interest. Applying the weighting procedure outlined by Wagenmakers and Farrell ([<reflink idref="bib43" id="ref35">43</reflink>]) to the dwelling age coefficients presented in this case study, the overall coefficient was equal to</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mo movablelimits="false">∑</mo><mi>m</mi></msub></mrow><mrow><mrow><mrow><mo stretchy="false">(</mo></mrow></mrow><mrow><msub><mrow><mrow><mi>β</mi></mrow></mrow><mrow><mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">E</mi></mrow></mrow></mrow></msub></mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">w</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">i</mi></mrow></mrow></msub></mrow><mo stretchy="false">)</mo></mrow></math> </ephtml> , where</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mrow><mi mathvariant="normal">w</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">i</mi></mrow></mrow></msub></mrow></math> </ephtml> was the weight for model <emph>i</emph> (= 1, ..., M). The weights were calculated as</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mrow><mi mathvariant="normal">w</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">i</mi></mrow></mrow></msub></mrow><mspace width="thinmathspace" /><mrow><mrow><mo>=</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi></mrow></mrow><mfenced open="(" close=")"><mrow><mrow><mrow><mo>−</mo><mn>0</mn></mrow></mrow><mrow><mrow><mn>.5</mn></mrow></mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">Δ</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">i</mi></mrow></mrow></msub></mrow></mrow></mfenced><mrow><mrow><mrow><mo>/</mo></mrow></mrow></mrow><munder><mrow><mo>∑</mo></mrow><mrow><mrow><mi mathvariant="normal">m</mi></mrow></mrow></munder><mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><mo>−</mo><mn>0</mn></mrow></mrow><mrow><mrow><mn>.5</mn></mrow></mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">Δ</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">m</mi></mrow></mrow></msub></mrow><mo stretchy="false">)</mo></math> </ephtml> , <emph>where</emph></p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mrow><mi mathvariant="normal">Δ</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">i</mi></mrow></mrow></msub></mrow></math> </ephtml> <emph>is the difference between the AIC value for model i</emph> and the best-fitting model of M (i.e., smallest AIC value). Implementing this procedure, we found that the model averaged dwelling age coefficient was approximately equal to −0.01 (Figure 2). This is considerably closer to zero than almost all of the regression coefficients identified in this article, suggests that the spatial regression models featuring all predictor variables provided the strongest support for the observed data, and supports the AIC values presented in Figure 2 showing that the models with dwelling age coefficient estimates closest to zero had substantially smaller AIC values (and better model fit) than those with larger negative coefficient estimates.</p> <p>More broadly, the specification curve can be used to highlight discussions around research reproducibility, replicability, and publication bias. In graduate classes focused on quantitative methods, the specification curve may be used as a pedagogical tool to interrogate an existing published result, perhaps by obtaining similar data, constructing a set of plausible models with different specifications that address the same research question, and checking the results of these models via a specification curve to investigate the impacts of model specification. While this has been used to explore published research in fields such as psychology (Frey et al., [<reflink idref="bib20" id="ref36">20</reflink>]; Rohrer et al., [<reflink idref="bib35" id="ref37">35</reflink>]) and economics (Cohen-Cole et al., [<reflink idref="bib13" id="ref38">13</reflink>]; Sala-i-martin, [<reflink idref="bib37" id="ref39">37</reflink>]), the specification curve has not yet been considered for spatial data analyses and in geographical education. This may be particularly informative when teaching about spatial weight matrices, the underlying assumptions of spatial weights, and the various approaches that can be used to conceptualize, formalize, measure, and specify spatial weight values.</p> <hd id="AN0156218662-9">Disclosure statement</hd> <p>No potential conflict of interest was reported by the authors.</p> <ref id="AN0156218662-10"> <title> Note </title> <blist> <bibl id="bib1" idref="ref31" type="bt">1</bibl> <bibtext> The data is available from GeoDa, a popular spatial analysis software package, and is used in the GeoDa handbook to teach spatial data analysis (Anselin, [2]).</bibtext> </blist> </ref> <ref id="AN0156218662-11"> <title> References </title> <blist> <bibtext> Anselin, L. (1988). Spatial econometrics: Methods and models. Kluwer Academic Publishers.</bibtext> </blist> <blist> <bibl id="bib2" type="bt">2</bibl> <bibtext> Anselin, L. (2003). GeoDa 0.9 User's Guide. Spatial Analysis Laboratory (SAL). 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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Using the Specification Curve to Teach Spatial Data Analysis and Explore Geographic Uncertainties
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kedron%2C+Peter%22">Kedron, Peter</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-1093-3416">0000-0002-1093-3416</externalLink>)<br /><searchLink fieldCode="AR" term="%22Quick%2C+Matthew%22">Quick, Matthew</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-1112-9323">0000-0002-1112-9323</externalLink>)<br /><searchLink fieldCode="AR" term="%22Hilgendorf%2C+Zach%22">Hilgendorf, Zach</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-0438-6516">0000-0002-0438-6516</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sachdeva%2C+Mehak%22">Sachdeva, Mehak</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0003-4375-5422">0000-0003-4375-5422</externalLink>)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Journal+of+Geography+in+Higher+Education%22"><i>Journal of Geography in Higher Education</i></searchLink>. 2022 46(2):304-314.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 11
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2022
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Evaluative
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Geography+Instruction%22">Geography Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Data+Analysis%22">Data Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Meta+Analysis%22">Meta Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+Making%22">Decision Making</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Software%22">Computer Software</searchLink><br /><searchLink fieldCode="DE" term="%22Instructional+Materials%22">Instructional Materials</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+%28Statistics%29%22">Regression (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Predictor+Variables%22">Predictor Variables</searchLink><br /><searchLink fieldCode="DE" term="%22Visual+Aids%22">Visual Aids</searchLink><br /><searchLink fieldCode="DE" term="%22Geographic+Information+Systems%22">Geographic Information Systems</searchLink><br /><searchLink fieldCode="DE" term="%22Information+Science%22">Information Science</searchLink><br /><searchLink fieldCode="DE" term="%22Housing%22">Housing</searchLink><br /><searchLink fieldCode="DE" term="%22Goodness+of+Fit%22">Goodness of Fit</searchLink><br /><searchLink fieldCode="DE" term="%22Costs%22">Costs</searchLink><br /><searchLink fieldCode="DE" term="%22Ownership%22">Ownership</searchLink><br /><searchLink fieldCode="DE" term="%22Generalization%22">Generalization</searchLink><br /><searchLink fieldCode="DE" term="%22Publications%22">Publications</searchLink><br /><searchLink fieldCode="DE" term="%22Bias%22">Bias</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Maryland+%28Baltimore%29%22">Maryland (Baltimore)</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/03098265.2021.1901076
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0309-8265<br />1466-1845
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Educational materials focused on spatial data analysis often feature mathematical descriptions of methods and step-by-step instructions of software tools, but infrequently discuss the set of decisions involved in specifying a statistical model. Failing to consider model specification may lead to specification searching, or the process of repeating analyses to obtain results that meet the criteria thought to be required for publication, and the disproportionate reporting of false-positive results in the academic literature. This article proposes that the specification curve -- a meta-analytical technique that visualizes the specifications and results from a large set of justifiable and plausible statistical models -- be used as a pedagogical tool to teach (spatial) data analysis and explore the geographic uncertainties that arise when specifying and interpreting spatial regression models. An example specification curve that focuses on two common specification decisions in a spatial regression model, specifically selecting predictor variables and constructing the spatial weight matrix, is illustrated. Strategies for using the specification curve in educational contexts to develop analytical plans, reflect on the generalizability of research findings, and highlight issues of replicability and publication bias are proposed.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2022
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1344171
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1344171
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/03098265.2021.1901076
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 304
    Subjects:
      – SubjectFull: Geography Instruction
        Type: general
      – SubjectFull: Data Analysis
        Type: general
      – SubjectFull: Meta Analysis
        Type: general
      – SubjectFull: Decision Making
        Type: general
      – SubjectFull: Computer Software
        Type: general
      – SubjectFull: Instructional Materials
        Type: general
      – SubjectFull: Teaching Methods
        Type: general
      – SubjectFull: Regression (Statistics)
        Type: general
      – SubjectFull: Predictor Variables
        Type: general
      – SubjectFull: Visual Aids
        Type: general
      – SubjectFull: Geographic Information Systems
        Type: general
      – SubjectFull: Information Science
        Type: general
      – SubjectFull: Housing
        Type: general
      – SubjectFull: Goodness of Fit
        Type: general
      – SubjectFull: Costs
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      – SubjectFull: Ownership
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      – SubjectFull: Publications
        Type: general
      – SubjectFull: Bias
        Type: general
      – SubjectFull: Maryland (Baltimore)
        Type: general
    Titles:
      – TitleFull: Using the Specification Curve to Teach Spatial Data Analysis and Explore Geographic Uncertainties
        Type: main
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      – PersonEntity:
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            NameFull: Kedron, Peter
      – PersonEntity:
          Name:
            NameFull: Quick, Matthew
      – PersonEntity:
          Name:
            NameFull: Hilgendorf, Zach
      – PersonEntity:
          Name:
            NameFull: Sachdeva, Mehak
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2022
          Identifiers:
            – Type: issn-print
              Value: 0309-8265
            – Type: issn-electronic
              Value: 1466-1845
          Numbering:
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              Value: 46
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Journal of Geography in Higher Education
              Type: main
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