1 Introduction

Behavioral health investigates behavioral problems impacting health such as physical inactivity (PI) (Kris-Etherton et al. 2021). PI is responsible for the deaths of approximately 3.2 million people per year and affects about 32% of the world's population aged 15 years and older (World Health Organization (WHO) 2020). The costs associated with PI account for more than 11% of total healthcare expenditures in the USA and are estimated to be $117 billion in 2021 (US America Health Ranking). The WHO defines physical inactivity in adults as less than 150 min of moderate-intensity activity per week. Since the industrial revolution, new technologies have enabled people to reduce the amount of physical labor required to complete many daily tasks. Although those technological revolutions have benefited many populations around the world, they have come at a high cost in terms of PI 's contribution to the global epidemic of noncommunicable diseases, such as cardiovascular disease-related mortality (Amidei et al. 2022), mental distresses (Pears et al. 2022), and cancer-related mortality (Cao et al. 2022). Indeed, adults' occupational physical activity is decreasing, but their leisure-time physical activity (i.e., walking and cycling) is increasing (Hallal et al. 2012). However, only 22% of Americans report regular, sustained physical activity (activity of any intensity lasting 30 min or more five times a week) (US America Health Ranking 2022). Individuals' physical activity is defined by a variety of policy, social, economic, cultural, environmental, behavioral, and biological factors (Sallis et al. 2006; Xue et al. 2018). Moreover, gaps in physical activity surveillance persist in individual and neighborhood levels. Given that more than half of the world's population lives in cities with limited leisure time, understanding the neighborhoods' characteristics may aid in identifying factors that promote sedentary and inactive lifestyles on a city-wide scale (Faka et al. 2019).

PI as a context-dependent and cross-disciplinary behavioral health has been associated with socioeconomic and built-environment factors (Aljabri 2022; Prince et al. 2022; Rütte et al. 2013). In terms of the built environment, urban characteristics such as urban form (e.g., residential density and high connectivity street network), neighborhood safety, and green space (Xiao et al. 2022; Peng et al. 2021; Passi-Solar et al. 2020; Feng and Astell-Burt 2019; Andersen et al. 2018) have received increased attention due to their associations with PI, obesity, and cardiovascular disease (Adlakha et al. 2021; Sims et al. 2020; An et al. 2019; Lenhart et al. 2017; Xu et al. 2015; Unger et al. 2014). Evidence suggests that the built environment can positively or adversely influence health behaviors. For example, PI increases are associated with residential insecurity and unaffordability (Rodgers et al. 2019). In economic crises, cost-burdened low-income households have limited resilience, resulting in housing insecurity that harm health (Rodgers et al. 2019). While the house circumstance is a social and environmental determinant of health (Rofle et al. 2020), there has been little research on the relationship between household ownership and health. Rental housing is related to poor neighborhood quality (Harris 1999), residential unaffordability, instability (Desmond and Shollenberger 2015), eviction from rental housing resulting in loss of social capital and trust among neighbors, and a lack of social cohesion, all of which have an impact on population behavioral health (Cradock et al. 2009). Household ownership, on the other hand, improves neighborhood quality by fostering social ties among neighbors, increasing satisfaction (Le Boennec and Lucas 2022), and ensuring residential stability (Mohanty and Raut 2009). Hence, housing ownership is critical in determining neighborhood quality and should be investigated further in public health studies.

Recent PI studies (Prince et al. 2022; Akinwumiju et al. 2022; Lee et al. 2017) have improved our understanding of the reasons of a significant increase in PI locally, globally, and in the United States. Typically, most PI research relies on linear aspatial models (i.e., Moreno-Llamas et al. 2021) and linear spatial models (i.e., Lane and Davis 2022; Kim and Kim 2021). However, nonlinear spatial models are rarely used to investigate relationships between tract-level PI prevalence and socioenvironmental factors. In one of those cases, Yang et al. (2021) studied the nonlinear effects of streetscape greenery on the walking behavior of older adults using a convolutional neural network (CNN) to evaluate human-scale, eye-level streetscape greenery. Although deep learning and artificial neural networks provide excellent predictive performance, they do not reveal how each variable affects the output. Moreover, geospatial technologies such as geographical positioning systems (GPS) are used to study people’s physical activities (i.e., Ramírez et al. 2021; Wang et al. 2021; Li 2021) that are leading to highly complex datasets, for which nonlinear solutions can be beneficial, especially when predictive performance is one of the objectives.

This study aims to introduce geographical random forest (GRF), a recently developed spatial machine learning algorithm into PI studies. The GRF is a decision tree-based nonparametric machine learning model (Georganos et al. 2021). It was recently developed to address the limitations of aspatial machine learning models and provide a modeling alternative to GWR approaches as it does not assume local linearity. The GRF model is similar to the GWR in concept, except that it is calibrated using random forests rather than an ordinary least squares regressors. It may also have superior predictive power and be used to evaluate associations between independent and dependent spatial variables by calculating variable importance (Georganos and Kalogirou 2022). Following that, each variable can be ranked from most to least important, tracing associations between independent and dependent variables.

GRF was recently used to model mean household income related to tertiary education, unemployment rate, and employment in the European Union regions (Georganos and Kalogirou 2022). Also, it was used to model and map the relative importance of 29 socioeconomic and health-related factors to the COVID-19 death rate, outperforming commonly used local and global regression methods such as OLS and GWR (Grekousis et al. 2022). It was also applied to predict diabetes prevalence in the USA (Quiones et al. 2021). However, more evidence is needed to investigate GRF use in other geographic contexts.

As a case study, we use Chicago, IL, USA, where nearly two out of every three adults (69%) are overweight or obese (US CDC 2021). While PI studies have previously relied heavily on traditional linear methods such as GWR and MGWR (Lee et al. 2017; Akinwumiju et al. 2022), this study applies state-of-the-art novel methods that have not been used in the specific domain before and introduces spatial machine learning to an audience that is typically not exposed to. Hence, the purpose of this study is to demonstrate how the recently developed GRF model can be used as a predictive and exploratory tool to investigate PI spatial heterogeneity while taking into account the nonlinear relationship between socioenvironmental factors and PI prevalence. This strategy can be used in various situations where independent variables can have varying predictive capacity and associations across space. To ensure the robustness of the experiments, the results are compared to the recently developed geographically weighted artificial neural networks (GWANN) (Hagenauer and Helbich 2022).

2 Data and method

2.1 Data

We obtained model-based estimates of current PI among the population over the age of 18 for all 793 census tracts in Chicago (“Physical inactivity” dependent variable). Based on responses to the Behavioral Risk Factor Surveillance System survey, the Centers for Disease Control and Prevention's PLACES Project provides statistics on PI as well as many other health-related metrics (US CDC 2021). PI is defined as the proportion of people who report doing no physical activity in their spare time. To obtain PI data, respondents were asked to answer the following question via a telephone survey: “Did you engage in any physical activities or exercises, other than your regular job, such as jogging, calisthenics, golf, gardening, or walking for exercise during the previous month?”.

As independent variables to the models, we utilize a poverty indicator (“Poverty” variable) based on income thresholds for those living below the poverty line, the unemployment ratio (“Unemployment” variable), and the eviction rates (“Eviction rate” variable). The eviction variable is constructed as the filings per renter-occupied households to the corresponding census tract population by the Chicago Health Atlas (CHA 2021). The threat of eviction has an impact on behavioral health as well as mental health due to anxiety and depression of household instability (Vásquez-Vera et al. 2017). Second, we quantified green space (“Green space” variable) as the mean of the green space index per census tract using the Normalized Difference Vegetation Index (NDVI) data from Landsat 8 NASA Earth Data (Google Earth Engine; Chander et al. 2009). In this study, urban green areas include any vegetation in the urban environment, including parks, green open spaces, residential gardens, mangroves, street trees, and green infrastructure (Labib et al. 2020). Furthermore, we quantified crime (“Crime ratio” Variable) using data provided by the Chicago Data Portal (CDP 2021) as the ratio between the number of crimes and the corresponding census tract population. Lastly, we provided the average percentage of owners per household (“Owners per household” variable) and the average percentage of renters per household (“Renter per household” variable) from the Location Affordability Index provided by the US Department of Housing and Urban Development (HUD 2021). As a final step into the preprocessing of the dataset, we examined the dataset for multicollinearity and ensured that correlation among independent variables did not lead to variance inflation. To do so, we calculated the variable correlation matrix and confirming that the variance inflation factors were below the recommended threshold of 2.5 (Cranley and Surles 2002).

With an average size of 0.28 square miles (standard deviation [SD] ± 0.39), census tracts were presumed a suitable analytical scale for assessing area-level physical inactivity prevalence. Census Tracts are small, permanent statistical subdivisions of a county according to the United States Administrative Divisions. Census tracts contain around 4000 people and are more demographically homogeneous, revealing more about local activities. The census tract-level variables were linked to the geometries via their 11-digit FIPS codes (US ACS 2019).

2.2 Methods

2.2.1 Random forest and geographical random forest

Breiman (2001) introduced random forest (RF), a nonparametric machine learning technique. RF is a grouping of independent decision trees that have been trained and tested for classification and regression problems. For each decision tree, a subset of training data is created through random sampling with replacement from the original training set (usually, two-thirds of the training set is used). Additionally, a random subset of predictor variables is picked for each node in each decision tree. A forest of trees is ultimately trained through the process described above with random subsets of training data points and predictors. Finally, each tree's prediction or classification error is computed, and all trees' final output is the average prediction value.

In the out-of-bag (OOB) set, the leftover data (the proportion of the data that is not sampled for training the trees) are used for internal evaluation and independent accuracy indicators. The RF OOB accuracy is a robust indicator frequently used to evaluate each variable's relevance and overall model performance (Breiman 2001). The increase in mean square error (IncMSE) is a typical metric for determining the relevance of a variable (Georganos et al. 2021). The OOB error is calculated by randomly permuting the values of each variable in the OOB set. If the OOB error increases, the variable is important, and the greater the change, the more relevant the variable is in estimating the dependent variable (Grekousis et al. 2022).

One of the most useful characteristics of an RF is its ability to determine the relative importance of each independent variable. In other words, it establishes which variable influences the dependent variable most. RF makes no statistical assumptions about the distribution of the data. As a result, it is better suited to dealing with variables with nonlinear correlations. Nonetheless, it still remains a global model, where spatial variations might not be accounted for, hindering both prediction and inference. The geographical random forest (GRF) model is a recent approach for modeling nonlinear and spatially heterogeneous relationships. GRF employs a spatial weights matrix and is locally calibrated using only nearby observations via a spatial kernel. In other words, a local RF is created and evaluated for each location based on input data from neighboring spatial units. GRF quantifies the local feature importance for each predictor in each local random forest model and the local residuals and goodness of fit (training and OOB). In addition, partial dependence plots were used to characterize the nonlinear relationships between the PI prevalence and the covariates. The partial dependence plots reveal whether the relationship between the target and a covariate is linear, monotonic, curvilinear, or more complex by presenting the expected target response as a function of the input covariate of interest (Friedman 2001). Georganos and Kalogirou (2022), Grekousis et al. (2022) and Georganos et al. (2021) provide comprehensive presentations of GRF regarding procedures, overfitting issues, and confounding variables. In this study, we also compared the results of the GRF with MultiScale geographical weighted regression (MGWR) (Oshan et al. 2019) to investigate the effectiveness of the machine learning models. The MGWR model produces the local R2, the local residual, and the set of local coefficients for each spatial unity. This allows for analyzing the spatial variation of associations between dependent and independent variables. On the other hand, GRF yields the local feature importance for each predictor in each local random forest model, the local residuals, and the local goodness of fit (training and OOB) (Kalogirou and Georganos 2022). Because the optimal bandwidth may vary across the predictors and is a priori unknown, we employed a MGWR, whereas each predictor variable has its own bandwidth (Iyanda and Osayomi 2021). This allows the scale of relationship non-stationarity to vary for each response-to-predictor variable relationship.

2.2.2 Geographically weighted artificial neural network

Artificial neural networks (ANNs) are machine learning (ML) models that have gained popularity in the computer vision field over the last decade and typically outperform traditional statistical models in terms of predictive power (Dave and Dutta 2014). The ANN is a network of interconnected nodes inspired by the simplification of neurons in the brain. A network of neurons with unidirectional connections allows a simulation of brain features to identify patterns and detect associations within data (Abiodun et al. 2018).

Multiple layers of neurons may be contained in an ANN model. The “input layer” is the first layer, and the “output layer” is the last, with "hidden layers" in between where neuronal weights define and express the link between inputs and outputs (Dongare et al. 2012). A single neuron in the next layer connects a group of neurons in the previous layer, while each layer transforms input values and defines neuronal weights. Hyperparameters such as the learning rate, number of hidden layers, and batch size should all be adjusted before running the model. The number of nodes in hidden layers, or the number of hidden layers depends on the problem at hand. Broadly speaking, the more complex the problem at hand, the more hidden neurons are needed; if the problem is linear, i.e., the relationship between dependent and independent data is linear, no hidden neurons are required. With regard to the number of hidden layers, NNs with just one hidden layer are commonplace when tabular data are used to solve a problem. In fact, the universal approximation theorem states that NNs using just one hidden layer can approximate any continuous function on compact subsets of \({\mathbb{R}}^{n}\) with arbitrary accuracy (Cybenko 1989; Hornik et al. 1989). However, in some cases, using more than one hidden layer can be convenient. For instance, deep NNs that utilize hundreds of hidden layers have been successfully applied in the domain of image and audio processing (e.g., LeCunn et al. 2015; Goodfellow et al. 2016).

Additionally, the batch size determines how many samples will be trained to estimate the error gradient before the model weights are updated. Gradient descent is used to train neural networks to find the best parameters that minimize the model's error. Learning rate is all about adjusting the weights of neurons and synapses (junctions between two neurons) to increase the accuracy of the outcome by minimizing observable errors. Although a high learning rate reduces training time, it also reduces ultimate accuracy (Abiodun et al. 2018).

A geographically weighted artificial neural network (GWANN) is similar to a basic ANN (Haykin 2008) except for two properties. First, each output neuron of a GWANN is assigned to a geographic location for which a prediction is to be made. This enables the computation of the spatial distances between the observations and the positions of the output neurons. Second, rather than the standard quadratic error function, GWANN calculates an error signal using a geographically weighted error function. That is, the difference between the output neurons' output and the target values is weighted by the spatial distance between the output neurons' location and the observation; when the location and observation are close together, the difference is given more weight than when they are farther apart. It is important to note that the number of target values and output neurons must be the same. For a thorough presentation of the GWANN formulas, see Hagenauer and Helbich (2022).

2.2.3 Parameter tuning

GRF uses a spatial weights matrix and is calibrated locally using only nearby observations through a spatial kernel. This study used the adaptive spatial kernel to estimate the optimal number of nearest neighbors as it is the most widely used and more appropriate when sampling is not uniform, such as census tracts of varying sizes in this case. In more detail, for each location, a local RF model is created based on input data of neighboring spatial units, in a similar fashion to GWR. Following the example of others (Grekousis et al. 2022; Quinones et al. 2021), we optimized the hyperparameters of GRF (‘number of variables randomly sampled (mtry)’, and ‘number of trees (ntree)’) using Random Grid Search (RGS) on the RF model (using CARET library in R). We then kept these hyperparameters fixed on GRF and initialized models with varying bandwidth sizes and selected the one with the highest OOB R2. The following variables were used to train the GRF: bandwidth = 22, “mtry” = 2, and “ntree” = 4000. Both global and local RF models were trained with the initial dataset to explore variation in feature importance due to the data distribution. Similar to RF, we ranked the variables’ importance based on the percent change in the MSE (Georganos et al. 2021). For predictions, a weight parameter is defined that fuses local and global estimates for the GRF model.

For the GWANN modeling, the input variables were scaled to have a zero mean and unit variance to facilitate the learning process. We adopted Nesterov's accelerated gradient (Sutskever et al. 2013) to adjust the connection weights with a momentum coefficient of 0.90. The learning rate of GWANN was set at 0.05, and the mini-batch size was set to 50. We used a single hidden layer consisting of eight hidden neurons. In addition, a bias neuron is added to the input and hidden layer. For the hidden neurons, the hyperbolic tangent function is employed as an activation function. We then kept these hyperparameters fixed and applied random grid search (RGS) with tenfold cross-validation on GWANN to find the best values for the bandwidth “bw,” which was found for a value of 3. To illustrate, a bandwidth of 3 means that the kernel bandwidth for estimating the parameters for a location equals the distance of this location to its third neighbor. It is important to note that small k does not necessarily mean “very local,” because k depends on the density of the data. For instance, if the data are very sparse, the kernel for a small k will encompass a larger geographic area than if the data are very dense. In addition, we used cross-validation to ensure that the models do not overfit. If the model would overfit due to a small kernel size (i.e. k = 3), the cross-validation score would be very poor and hence such a small kernel size would not be considered. Moreover, due to the Gaussian kernel, all locations are always considered but with varying degrees. GWANN does not make any assumption about the statistical distribution of the data and considers spatial heterogeneity. As a result, it is better equipped to handle variables which have nonlinear correlations that vary spatially.

2.2.4 Validation

To test the predictive performance of models, we used 10 randomly chosen splits of the data with 90% retained for training the models and 10% of the data held back for testing. Specifically, the data set (n = 793) was randomly split into 713 training data objects used to train the models and 80 test data objects used for evaluating the model performance. We then computed performance metrics such as the MSE, RMSE, and coefficient of determination (R2). Lastly, we reported the average value of these metrics over the 10 iterations.

2.2.5 Spatial autocorrelation

We use local Moran's I to assess residual spatial autocorrelation and track potential clustering in the residuals of the models (Anselin 1995) using the full census dataset.

2.3 Software

All our statistical analyses were conducted on the “SpatialML” package (Kalogirou and Georganos 2022) and the “GWANN” package (Hagenauer and Helbich 2022) in R Statistical Computing Environment (R Core Team 2020), and for cartography, the ArcGIS 10.8.1 was used.

3 Results

Figure 1 illustrates the prevalence of PI and socioecological variables at the tract level. PI is more common in Chicago's southern and western neighborhoods. Chicago's south side has the highest crime rate. Poverty, eviction, and unemployment are also more prevalent in the south and west. The greenest areas are in the neighborhoods to the south and far north. Except in downtown areas, the city's population of renters and house owners is fairly consistent.

Fig. 1
figure 1

Descriptive maps of physical inactivity prevalence and hypothesized socioecological determinants

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Partial dependence plots (PDPs) were extracted from the random forest model to characterize the nonlinear relationship between the predictor variables and PI prevalence (Fig. 2). All characteristics, such as crime ratio (Fig. 2a), green space (Fig. 2d), and renters per household (Fig. 2f), have a curvilinear relationship with PI prevalence. Linear correlations exist between variables, but only within specific ranges. There is a positive linear link between eviction rate and PI prevalence in the range 0.5–1 (Fig. 2e). Similarly, in range 5–6, there is a linear positive link with poverty and PI prevalence, but the effect reduces after that (Fig. 2b). The data show that nearly all associations are nonlinear, highlighting the need of utilizing nonlinear regression models.

Fig. 2
figure 2

Partial dependency profiles of the determinants of the random forest model

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The GRF model had lower MSE values and a higher local R2 in the out-of-sample predictions (OOB set) than the global RF model (Table 1). Table 1 shows that the R2 and MSE from RF and GRF are very close, implying that the global model developed by RF may be valid for describing the relationships between the PI and the covariates. The GFR model should be used to test local variations of the relationships. According to the permutation-based feature importance, poverty is the most important feature, followed by unemployment (PFI) in both models. As shown in Table 1, the importance ranking of determinants in GRF can differ from that of the global RF model. Renters per household, for example, are ranked third in the RF model (higher IncMSE) but fifth in the GRF model (lower IncMSE). Similarly, in the RF model, the crime ratio is ranked fifth, but third in the GRF model (Table 1). Nonetheless, it is important to note that the ranking of the GRF approach is based on the mean value of the whole local distribution of feature importance.

Table 1 Summary results of random forest (RF) and geographically random forest (GRF) models
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Additionally, the MGWR model (AICc = 116.27, RSS = 36.02) exhibited an adjusted R2 of 0.88. The Moran’s I test (I = −0.01 p = 0.15) of MGWR turns out to be statistically insignificant confirming a lack of residual spatial autocorrelation congruent with the model assumption (Supplemental Fig. 1.). Supplemental Fig. 2 illustrates the MGWR model covariates’ variation. The optimal bandwidth ranges from 44 to 487 per census tract, suggesting that the independent variables operate on different scales. It shows that the independent variables “green space,” “eviction rate,” and “renters per household” operate on a small spatial scale compared to “crime ratio,” “owners per household,” “unemployment,” and “poverty”.

In addition, the importance of the determinants was mapped to understand to better visualize and understand potentially interesting local variations (Fig. 3). The importance of crime ratio (Fig. 3a) is the largest in a few places in the Mideast along Lake Michigan and southwest. Poverty, on the other hand, is important throughout the city, particularly in the south, southwest, mid-north, and northeast (Fig. 3b). Similarly, unemployment is more prevalent in the south and west downtown, and a few places in the southwest neighborhoods of the city (Fig. 3c). However, the green space predominately has the lowest importance except for some neighborhoods of the west downtown (Fig. 3d). The importance of eviction rates and renters per household is highest in a few places of south, southwest downtown, and mid-north (Fig. 3e and f). However, the importance of owners per household is highest in the south downtown with a few places in the northwest and northeast (Fig. 3g). Overall, Fig. 3 demonstrates the importance of unemployment, green space, eviction rate, renters, and owners per household determinants in a few south downtown neighborhoods on PI prevalence. This strategy aids in identifying the combination of variables strongly associated with PI prevalence in a few neighborhoods, which is extremely useful for policymakers and health professionals in developing related policies to address place-based interventions.

Fig. 3
figure 3

Spatial variation of local feature importance (IncMSE), highest positive values showing strongest importance

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3.1 Predictive performance of linear and nonlinear models

We found that the GRF and GWANN models performed similarly, with a slight GWANN outperformance, based on our independent validation approach (Table 2). The GWANN model accounts for somewhat higher PI variability (R2 = 0.92) than the GRF model (R2 = 0.91) while reducing overall RMSE values (0.26 vs. 0.27). Both models outperform the RF model. Notably, GRF quantifies the local feature importance for each predictor in each local random forest model, which is extremely valuable from the standpoint of geographical analysis.

Table 2 Evaluation of the predictive performance of models based on the test dataset
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To further understand how GWANN, GRF, and RF handled geographical heterogeneity, we show the spatial distribution of the local residuals (Fig. 4). We also utilize local Moran's I to look for potential clustering in the residuals and estimate spatial autocorrelation. GWANN and GRF have addressed spatial heterogeneity in most cases. Residuals of GWANN and GRF are not geographically clustered in most places and are randomly dispersed. Notably, for GRF, the residuals are based on pseudo-hold-out predictions of the OOB sample and not a direct fit on the training data.

Fig. 4
figure 4

Spatial distribution of the models’ residuals and local Moran's I of residuals per model

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4 Discussion

This cross-sectional socioecological study investigates the prevalence of PI at the tract level. The nonlinear regression models GWANN and GRF were used. While GWANN is a black-box model that is complex enough to be incomprehensible to humans, GRF is used to supplement interpretability by identifying elements that cause local variations in PI prevalence rates, as demonstrated by other studies (Georganos et al. 2022; Georganos et al. 2021; Luo et al. 2021). This study examines machine learning models for predicting PI prevalence and the spatial importance of neighborhoods’ socioecological determinants in PI studies. Neighborhood characteristics account for three of the top four most important local factors (poverty, unemployment, and crime), while one is related to housing (eviction rate). The implications of the findings regarding these determinants are discussed further.

4.1 Poverty

Poverty is the most important factor in the large percentage of Chicago's census tracts (Fig. 4b). Although poverty is a multidimensional feature that encompasses the various deprivations that people face in their daily lives (Aktinson et al. 2002; Alkire and Apablaza 2016), it is explicitly associated with low income (financial poverty) and a variety of non-monetary factors (i.e., poor health, poor urban services) (United Nations 2016). Poverty is more important in neighborhoods where the population is overwhelmingly socially disadvantaged. Poor people frequently bear a double burden: they must deal with both the multiple harms caused by their own lack of income and the social consequences of living in a poor neighborhood (Vallée et al. 2022), such as the vulnerable African-American population in south Chicago neighborhoods (Mendenhall 2018). The mental distress and anxiety in these places have an impact on behavioral health as well as physical activity (Copeland and Snyder 2011). In poor neighborhoods, health disparity worsens with lack of access to affordable, healthy foods, living in overcrowded areas with poor sleep quality, high rent burdens, and household instability, which discourage healthy behaviors (Stanley et al. 2022; Kwarteng et al. 2017). Additionally, low-income neighborhoods lack access to well-designed green spaces, open spaces, sidewalks, and sports equipment to engage in physical activities (Huston et al. 2003). Hence, it is primarily critical to understand the “leisure-time physical activity” definition among socially vulnerable people because their daily lives are pounded with economic instability. Additionally, the relationship between poverty and physical activity is not well understood or direct, and more research is required (Armstrong et al. 2018).

4.2 Unemployment

Unemployment is highest per census tract in the southern downtown places near Lake Michigan, as well as in a few places on the west side of downtown (Fig. 4c). Unemployment has long been associated with a higher risk of disease (e.g., Miao et al. 2021). This association is rarely explained by behavioral health such as physical inactivity, risk of overdose (Sawyer et al. 2021), exacerbated by lower income and psychological stress (Jin et al. 1995).

Further studies should investigate employment status (full-time, part-time, unemployed) and job type (active and sedentary) in behavioral health studies, because unemployed people, according to Gryson (1993), are just as active as employed people. Brown and Trost (2003) found that higher PI is associated with employment. In this sense, one's job has a little direct effect on the prevalence of PI. Furthermore, Marrone and Swarbrick (2020) found that long-term unemployment has a significant negative impact on population behavioral and mental health. As a result, the duration of unemployment should also be considered in public health studies.

4.3 Crime

The importance of crime per census tract is strongest in the southern downtown districts (Fig. 4a), where eviction rate and poverty are relatively high (Fig. 1e and b). The community and individual-level factors associate PI with neighborhood crime. Business withdrawal, population out-migration, physical deterioration, declining community resources, and crumbling public infrastructure are witnessed at the community level in high-crime zones that are unsafe for physical exercise (Feuillet et al. 2020; Lacoe et al. 2018). Also, individuals' perceptions of unsafety, anxiety, and stress are influenced by neighborhood crime, which restricts participation in physical activities (Park and Garcia 2020). In this study, crime refers to a variety of illegal behaviors. However, outdoor and indoor crimes and types of crimes (home burglary vs. robbery) should be treated separately when dealing with crime issues at the neighborhood level. Overall, well-planned with a well-maintained built environment (e.g., green spaces) can discourage illegal behavior. The term "well-planned" refers to areas with the capacity for informal and formal social control and thus provide safety (Weisburd et al. 2021).

4.4 Eviction rate

The eviction rate per census tract is most important in the southern neighborhoods along Lake Michigan (Fig. 4e), which have a high poverty rate and a share of green spaces (Fig. 1b and d). Housing insecurity and unaffordability can lead to stress and despair, as well as alter metabolism and increase the risk of unhealthy behaviors such as smoking and inactivity (Chambers and Fuster 2012; Hazekamp et al. 2021). Little is known about how policy interventions, such as supply-side housing subsidy programs aimed at increasing affordable housing, affect eviction dynamics in communities across the United States (Preston and Reina 2021). Our findings highlight the importance of local governments acting quickly to protect public health from the PI and obesity epidemics by increasing rental assistance and extending the eviction moratorium (Chicago Eviction 2022).

Although other socioecological variables in this study (green space, renters per household, and owners per household) had minor importance on the prevalence of PI in Chicago, green space that is available, visible, and accessible can improve the function of green space in boosting population health by encouraging physical activity participation. However, rather than focusing on green infrastructure to improve health, Chicago, and other large cities develop and plan green spaces with the tourism industry in mind. Additionally, there is insufficient research on the impact of the number of renters versus owners per household on developing a healthy and friendly neighborhood environment that encourages social cohesion and inclusion. More research is needed on the house as a social and environmental determinant of health for individuals and communities.

4.5 Limitations

The tract-level estimates used in previous studies (e.g., Hohl and Lotfata 2022) have some limitations. While our findings may be affected by the underlying analytical scale, causal inference is also complicated by the data's cross-sectional and ecological nature (Helbich et al. 2021). A telephone survey was used to collect the outcome variable, which is likely to have problems due to recall bias, social desirability bias, and the inability to reach households without landlines (US CDC 2021). Moreover, social, physical, spatial, cultural, personal, and interpersonal dynamics contribute to physical inactivity. However, the primary goal of this research is not to propose a holistic approach to model and map PI by taking into account every available factor, but rather to present new spatial methods to the community for improving the prediction of health outcomes. In addition to the data limitation, locally weighted models have some drawbacks. To train the GRF that accounts for differences in tract size, for example, we used an adaptive kernel bandwidth to choose the optimal number of tracts. Tracts of varying sizes dispersed across a geographic area may result in dependent variable spillover effects or residual spatial autocorrelation. The local R2 in the GRF varied across space, as expected. The R2 was less than 0.5 in some tracts in the city's south, west, and north. These findings suggest that the variables included only explained a small portion of the variance in the outcome variable and that additional variables should be included to improve the performance of the local models in these regions. In terms of GWANN model, the inner workings of GWANN are hard to perceive by humans. More experimental experiments are required to extend GWANN to local analysis. Also, GWANN depends on many hyperparameters (number of hidden neurons, batch size, momentum, etc.), which were chosen for this study a priori. Hence, it is not guaranteed that the chosen hyperparameters yielded the best results. Determining optimal hyperparameters in an experimental setting, though, is cumbersome because it can be expected that the hyperparameters are not independent of each other.

5 Conclusion

This is the first study to look at the geographic variation in PI prevalence at the tract level in response to factors associated with neighborhood circumstances using the GWANN and GRF models. It is a significant finding regarding the usefulness and applicability of the GRF and GWANN spatial regression models in geographical analysis because they account for nonlinear relationships and address spatial heterogeneity. More importantly, GRF is used to determine how the importance of each variable varies spatially. Additionally, given the high likelihood of local collinearity, researchers are encouraged to use GWANN and GRF in population health studies to assess the effects of a wide range of socioecological data samples on behavioral health. As these models are prediction-oriented, they can be used to run different scenarios and projections which are vital components for enhancing evidence-based policy making.

The findings of this study could lead to more targeted epidemiologic research at the tract level, allowing researchers to better understand the mechanisms driving inactive lifestyle in different places with different household and neighborhood-related characteristics, particularly in Chicago, where obesity is the highest risk. Other elements of household quality (such as household composition, mobile homes, homelessness, and pollution), as well as the spatial behavior of the PI epidemic from a neighborhood health standpoint, should be investigated in future research. Understanding the spatial heterogeneity of PI determinants’ associations could lead to more advanced research and policy development in large US cities to address PI's underlying, spatially varied drivers at the local level.