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Within the last few years, geographers and researchers in other cognate disciplines with geographic concerns have begun to use multilevel models. While there are several useful existing introductory accounts of these models in the geographical literature, this paper seeks to extend them in three main ways to clarify and emphasize further the substa...
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... full results for this model are given in Table 2. As can be seen, all of the level-2 "The social class categorization used was based on that ap lied in the survey that follows the Registrar General's classification. ...
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... on the basis of a x2 test, all of the terms are sigdcant except the two "covariances" between the base category, I11 manual, and IV&V and Missing (the and oPw4 in Table 2 ...
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... already noted, when using categorical predictors based on dummy/indicator coding, values for the base category are estimated directly while those for the re- maining categories are estimated as differentials from these. Using xo to represent the base category, 111 manual, and x1 to x4 to represent the remaining categories-I&& I11 nonmanual, IV&V, and Missing, respectively-the between-ward variation for each sociil class category according to the model in Table 2 is given by Given that the predictor variables only take the value 0 or 1, the equations above re- duce to the appropriate random parameter(s). Thus, for the model in Table 2 we ob- tain the results shown in Table 3. ...
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... xo to represent the base category, 111 manual, and x1 to x4 to represent the remaining categories-I&& I11 nonmanual, IV&V, and Missing, respectively-the between-ward variation for each sociil class category according to the model in Table 2 is given by Given that the predictor variables only take the value 0 or 1, the equations above re- duce to the appropriate random parameter(s). Thus, for the model in Table 2 we ob- tain the results shown in Table 3. These results c o n k the interpretation just made. ...
Citations
... The former focuses on decomposing a single variable or measure as a function of itself, such as spatial variability (Oliver and Webster 1986;Collins and Woodcock 2000), moving window averages (Pigozzi 2004), the statistical likelihood (Kolaczyk and Huang 2001), diversity and dissimilarity indices (Wong 2003;Manley et al. 2019), or entropy (Phillips 2005;Batty 2010;Leibovici and Birkin 2015). In contrast, the latter focuses on decomposing a variable as a function of other variables (e.g., Duncan and Jones 2000). More recent work found in this review corpus extended these types of multilevel multiple regression models to examine contributions from different groups (i.e., categories) across scales (Manley et al. 2015), modeling spatially clustered survey data based on attributes of individuals, neighborhoods, wider regions, and heterogeneities across them (Ma et al. 2018), the development of hierarchical spatial autoregressive models to capture dependencies at each level (Dong and Harris 2015), and a locally adaptive extension (Dong et al. 2020). ...
... Since traditional multilevel models always incorporate multiple exogenously defined observation scales, they allow inferences to be made about the levels where one or more processes can be explained. There were several examples of traditional multilevel models in the corpus (e.g., Barnett 1973;Duncan and Jones 2000;Kolaczyk and Huang 2001;Dong and Harris 2015;Manley et al. 2015;Tian et al. 2015;Johnston et al. 2016;Malanson et al. 2017;Ma et al. 2018;Greene and Kedron 2018;Sun and Yin 2018;Manley et al. 2019), but few instances of multilevel models extended to become analogous to GWR and MGWR (i.e., spatially varying coefficient models) by searching across geographic scales (i.e., ranges) to allow process scale(s) to be expressed endogenously. The final examples in this box include techniques for calculating summaries across exogenously defined scales. ...
Scale is a central concept in the geographical sciences and is an intrinsic property of many spatial systems. It also serves as an essential thread in the fabric of many other physical and social sciences, which has contributed to the use of different terminology for similar manifestations of what we refer to as ‘scale’, leading to a surprising amount of diversity around this fundamental concept and its various ‘multiscale’ extensions. To address this, we review common abstractions about spatial scale and how they are employed in quantitative research. We also explore areas where the conceptualizations of multiple spatial scales can be differentiated. This is achieved by first bridging terminology and concepts, and then conducting a scoping review of the topic. A typology for spatial scale is discussed that can be used to categorize its multifarious meanings and measures. This typology is then used to distinguish what we term ‘process scale,’ from other types of spatial scale and to highlight current trends in uncovering aspects of process scale. We end with suggestions on how to further build knowledge regarding spatial processes through the lens of spatial scale.
... and 2) does spatial heterogeneity exist within rentals based on their origin station, given that each carsharing station has a different built environment and land use characteristics? To answer these questions, a multilevel mixed-effect modeling approach (Duncan and Jones, 2000) is applied to remedy the spatial clustering issue of outcome variables nested within a station location variable, as this approach allowed the estimation of multilevel-mixed effects such as members' personal and usage characteristics at level 1 and carsharing stations' locational characteristics at level 2 on traveled distance. Before the multilevel modeling, a classification of the carsharing members was conducted by a regression tree to obtain the most homogenous groups of members based on their traveled distance. ...
... In this study, we extend this relationship by taking into account the usage behavior of carsharing members and built environment characteristics of stations through estimation of a multilevel model that might recognize spatial issues similar to those discussed above. This modeling is also useful in addressing the recognized limitations of multiple and linear regression analyses that fail to capture variation within individuals and between places and used as an alternative approach (Bottai et al., 2006;Duncan and Jones, 2000;Páez et al., 2007). For example, in this study, 1,203 carsharing stations are used, each with distinctive locational characteristics, generating multiple rentals. ...
... where σ 2 u0 is the variance of the level-2 residuals and σ 2 e is the variance of the level-1 residuals. In other words, the ICC reports the amount of variance unexplained by model predictors (the portion of variance that exists between stations) compared to the overall unexplained variance in the traveled distance (Duncan and Jones, 2000). In the case of this study, the ICC accounts for the proportion of the total residual variation that is due to differences between carsharing stations. ...
Abstract
This study explores the mobility patterns of carsharing members from their trip distance perspective and its associated factors with a specific focus on its members' personal, usage, and stations' locational characteristics. Using Seoul as a case study, one-month rental transaction datasets provided by two-way carsharing operators were used as a data source. The multilevel mixed-effect modeling approach was applied to remedy spatial heterogeneity across station locations that affect the distance traveled by each rental. In addition, a classification among the carsharing members based on trip distance was conducted using regression tree to obtain clusters of the most homogenous member groups. The multilevel model results confirmed the important roles played by the station location and individual-level factors that affect mobility patterns of carsharing members. Individual-level characteristics showed that members in their 50s and female travel longer. Similarly, rentals made on non-workdays and in the morning showed longer travel distances. The station-level characteristics indicate that carsharing stations' proximity to public transit and leisure areas positively affects trip distances, suggesting the effect of the built environment and land use on the travel patterns of carsharing members. By combining carsharing transaction and their stations’ built environment data, this study suggests a new interface for city officials and carsharing operators to work together for achieving their sustainable mobility objectives together.
... Leverage is also included as a control variable because highly indebted firms are likely to have better sustainability practices (Orazalin & Mahmood, 2018). Finally, financial capacity is controlled because firms with greater financial resources are likely to have better sustainability practices with higher application levels (Reverte, 2009 A multilevel modeling analysis makes it possible to estimate unbalanced datasets and avoid biased estimates resulting from a small number of observations and sampling fluctuations (Duncan & Jones, 2000). In contrast to ordinary least squares (OLS) and other statistical approaches, multilevel modeling can analyze longitudinal data by taking into account both within-and between-firm variances when estimating the relationships between dependent and independent variables (Certo et al., 2017;Z. ...
The objective of this study is to examine the effects of board characteristics and country governance quality on both individual aspects and the overall level of environmental performance through the lens of agency, resource dependency, and institutional theories. The study is based on a sample of 3023 firm‐year observations from European companies operating in 22 countries between 2009 and 2016. Data on the resources, emissions, and innovation dimensions of environmental performance and board governance data were collected from the Refinitiv database, whereas financial data were extracted from the Worldscope database. The study employs a multilevel modeling analysis and the generalized method of moments (GMM) estimation technique to analyze the data. The findings suggest that board gender diversity and the presence of a corporate social responsibility and sustainability committee have a positive impact on environmental performance. The results also show that country governance quality is positively related to environmental performance. The findings have important implications for practitioners, regulators, and policymakers with respect to the effectiveness of corporate governance mechanisms and country governance systems in determining corporate environmental practices.
... We use multilevel regression models as proposed in geographical research to provide accurate estimates of the effects of individual and contextual factors on travel behavior (eg; Kim and Wang, 2015;Duncan and Jones, 2000;Páez and Scott, 2004;Mercado and Páez, 2009). The primary motive for using multilevel models is to be able to take into account the hierarchical structure of the data, in order to model their spatial heterogeneity. ...
This study analyzes gender differences in travel patterns for the Metropolitan Area of Montevideo, Uruguay. By applying multilevel regression models, it provides estimates of the impact of individual and contextual factors on travel behavior. The paper's findings lend support to the household responsibility hypothesis, which claims that women's travel patterns are affected by the type of household in which they live and the consequent responsibilities or roles they assume. Furthermore, gender differences in travel patterns are reinforced across census tracts. The results indicate that policy makers need to consider gender differences when seeking to enhance urban planning decisions.
... HLM is superior to singlelevel regression models and able to provide more accurate estimates, as the latter ignores the nested structure of the data and wrongly assumes independence of the observations and randomness of errors (Parboteeah et al., 2008;Terpstra-Tong et al., 2020). Moreover, HLM allows avoiding misestimation problems derived from sampling fluctuations and a small number of observations through higher levels of analysis (Duncan and Jones, 2000). Thus, with HLM, the unbalanced nature of the data set will not produce biased estimates and standard errors, which enhances the results' robustness (Ortas et al., 2020). ...
This multilevel study investigated the effect of national institutional environments on the relationship between corporate responsibility practices and financial performance in multiple European countries, controlling for firmlevel predictors. By doing so, we demonstrate that neither institutional theory nor stakeholder theory is adequate to investigate results in a multilevel study, which is becoming the norm of the 21st century businessworld. As such, we develop the multilevel-pressures theory designed to handle the demands of multilevel analyses. It synthesises the essences of these two theories and expands upon them. To test our multilevel hypotheses, we conducted a survey of 2622 firms from 18 European countries representing different institutional contexts in terms of societal governance, European Union integration, and economic conditions. Hierarchical linear modelling results indicated that, consistent with multilevel-pressures theory, national institutional contexts exert multilevel moderating effects on the relationships between investor, local community and environmental corporate responsibility practices and firms’ financial performance.
... HLM is superior to singlelevel regression models and able to provide more accurate estimates, as the latter ignores the nested structure of the data and wrongly assumes independence of the observations and randomness of errors (Parboteeah et al., 2008;Terpstra-Tong et al., 2020). Moreover, HLM allows avoiding misestimation problems derived from sampling fluctuations and a small number of observations through higher levels of analysis (Duncan and Jones, 2000). Thus, with HLM, the unbalanced nature of the data set will not produce biased estimates and standard errors, which enhances the results' robustness (Ortas et al., 2020). ...
This multilevel study investigated the effect of national institutional
environments on the relationship between corporate responsibility practices and financial performance in multiple European countries, controlling for fir-mlevel predictors. By doing so, we demonstrate that neither institutional theory nor stakeholder theory is adequate to investigate results in a multilevel study, which is becoming the norm of the 21st century businessworld. As such, we develop the multilevel-pressures theory designed to handle the demands of multilevel analyses. It synthesises the essences of these two theories and expands upon them. To test our multilevel hypotheses, we conducted a survey of 2622 firms from 18 European countries representing different institutional contexts in terms of societal governance, European Union integration, and economic conditions. Hierarchical linear modelling results indicated that, consistent with multilevel-pressures theory, national institutional contexts exert multilevel moderating effects on the relationships between investor, local community and environmental corporate responsibility practices and firms’ financial performance.
... Moreover, HLM allows avoiding misestimation problems derived from sampling fluctuations and a small number of observations through higher levels of analysis (Duncan and Jones, 2000). Thus, with HLM, the unbalanced nature of the dataset will not produce biased estimates and standard errors, which enhances the results' robustness (Ortas et al., 2020). ...
This multilevel study investigated the effect of national institutional environments on the relationship between corporate responsibility practices and financial performance in multiple European countries, controlling for firm-level predictors. By doing so, we demonstrate that neither institutional theory nor stakeholder theory is adequate to investigate results in a multilevel study, which is becoming the norm of the 21 st century businessworld. As such, we develop the multilevel-pressures theory designed to handle the demands of multilevel analyses. It synthesizes the essences of these two theories and expands upon them. To test our multilevel hypotheses, we conducted a survey of 2,622 firms from 18 European countries representing different institutional contexts in terms of societal governance, European Union integration, and economic conditions. Hierarchical linear modelling results indicated that, consistent with multilevel-pressures theory, national institutional contexts exert multi-level moderating effects on the relationships between investor, local community, and environmental corporate responsibility practices and firms' financial performance.
... Third, even if data were available on all 33 Service Areas, these areas could still prove to be too large to identify between-area differences in children's unmet need. Large areas of geography tend to be heterogeneous with low levels of between-area differences whereas small areas of geography tend to be homogeneous with higher levels of between-area differences (Duncan and Jones 2000). Indeed, a UK multilevel analysis of mental disorders only determined variability at the individual and household level and not at the electoral ward level and concluded that these wards were likely too large (Weich et al. 2003). ...
There is limited empirical evidence documenting the magnitude and correlates of area-level variability in unmet need for children’s mental health services. Research is needed that identifies area-level characteristics that can inform strategies for reducing unmet need in the population. The study purpose is to: (1) estimate area-level variation in children’s unmet need for mental health services (using Service Areas as defined by the Ontario Ministry of Children and Youth Services), and (2) identify area-level service arrangements, and geographic and population characteristics associated with unmet need. Using individual-level general population data, area-level government administrative data and Census data from Ontario, Canada, we use multilevel regression models to analyze unmet need for mental health services among children (level 1) nested within Service Areas (level 2). The study finds that 1.64% of the reliable variance in unmet need for mental health services is attributable to between-area differences. Across areas, we find that Service Areas with more agencies had a lower likelihood of unmet need for mental health services. Compared to other Service Areas, Toronto had much lower likelihood of unmet need compared to the rest of Ontario. Rural areas, areas with unsatisfactory public transport, and areas with higher levels of socio-economic disadvantage had a higher likelihood of unmet need for mental health services. These findings identify challenges in service provision that researchers, policymakers and administrators in children’s mental health services need to better understand. Policy implications and potential Service Area strategies that could address equitable access to mental health services are discussed.
... To address the aforementioned problems, a different spatial measurement method was developed by Dubin [19] and Harry et al. [61]. Additionally, a number of techniques have been proposed and developed to deal with spatially varying coefficients [62][63][64]. However, one of the most recent local regression approaches corresponds to mixed geographically weighted regression (mixed-GWR) introduced by Crespo and Grêt-Regamey [65]. ...
The main purpose of this paper is to use regression models to explore the factors affecting housing prices as well as apply spatial aggregation to explore the changes of urban space prices. This study collected data in Taitung City from the year 2013 to 2017, including 3533 real estate transaction price records. The hedonic price method, spatial lag model and spatial error model were used to conduct global spatial self-correlation tests to explore the performance of house price variables and space price aggregation. We compare the three models by R² and Akaike Information Criterion (AIC) to determine the spatial self-correlation ability performance, and explore the spatial distribution of prices and the changes of price regions from the regional local indicators of spatial association spatial distribution map. Actual analysis results show an improvement in the ability to interpret real estate prices through the feature price mode from the R² value assessment, the spatial delay model and the spatial error model. Performance from the AIC values show that the difference of the spatial delay model is smaller than that of the feature price model and the spatial model, demonstrating a better performance from the space delay model and the spatial error model compared to the feature price model; improving upon the estimation bias caused by spatial self-correlation. For variables affecting house pricing, research results show that Moran's I is more than 0 in real estate price analysis over the years, all of which show spatial positive correlation. From the LISA analysis of the spatial aggregation phenomenon, we see real estate prices rise in spaces surrounded by high-priced real estate contrast with the scope of space surrounded by low-cost real estate shifting in boundary over the years due to changes in the location and attributes of real estate trading transactions. Through the analysis of space price aggregation characteristics, we are able to observe the trajectory of urban development.
... This research tests the links of time series data for annual observa- (Duncan & Jones, 2000). Thus, the unbalanced nature of the dataset will not produce biased estimates and standard errors. ...
This paper studies the influence of different national institutions on corporate environmental, social, and governance (ESG) performance through the varieties of institutional systems approach. This research complements previous research that used traditional approaches such as the national business systems and the varieties of capitalism, because it considers companies in understudied economies in Asia, Africa, Eastern Europe, the Middle East, and Latin America. To that aim, a dataset of 4,751 firms within 52 countries is examined through a multilevel model, which allows establishing three levels of analysis: (a) yearly observations of a firm ESG performance, (b) the companies, and (c) the countries. This technique is useful to address the nested nature of firms' ESG performance within higher level institutional contexts. The results identify which specific national institutions enhance/restrict companies' ESG performance. This provides interesting implications because firms' ESG represent most of the companies' contributions to environmental preservation, social well‐being, and community development.
