Quantitative Assessment of Age-Friendly Design in Mountainous Urban Community Parks Based on Nonlinear Models: An Empirical Study in Chongqing, China

Abstract

As China undergoes a rapid transition into an aging society, the mobility challenges faced by the older adults in high-density mountainous cities are exacerbated by complex topographical conditions. Existing studies often overlook the nonlinear relationships and the distinct planning requirements of mountainous versus flat urban areas when evaluating the age-friendliness of community parks. This study aims to identify the critical elements of age-friendly planning in mountainous community parks, validate the applicability of nonlinear models, and quantify the dynamic effects of various factors on older adults’ satisfaction, thereby establishing a foundation for targeted optimization strategies. Utilizing principal component analysis (PCA) on 358 valid questionnaires collected from three representative mountainous community parks in Chongqing, six key planning factors were extracted. An ordered logit model was employed for regression and marginal effect analyses. The findings reveal that (1) the ordered logit model outperforms alternative models in terms of goodness-of-fit and computational efficiency, making it particularly suitable for capturing the nonlinear characteristics of satisfaction; (2) accessibility facilities, spatial and social connectivity, and landscape environment emerge as the primary determinants of older adults’ satisfaction, with improvements in accessibility facilities exerting the most significant impact; and (3) the provision of multifunctional activity spaces and increased social opportunities effectively addresses the psychological and physiological needs of the older adults. This study contributes to the optimization of age-friendly design strategies for community parks in high-density mountainous cities, offering valuable insights for promoting healthy aging and fostering inclusive urban environments.

1. Introduction

As global population aging accelerates, the development of inclusive urban environments has become central to achieving the United Nations Sustainable Development Goal (SDG 3) of ensuring “good health and well-being for all ages” [1]. China, one of the fastest aging countries, is projected to have its older adult population exceed 30% by 2035 [2], with cities like Chongqing, characterized by high population density and mountainous terrain, already exhibiting a significantly higher proportion of older adults than the national average [3]. The spatial fragmentation and considerable vertical elevation differences resulting from complex topography in these cities limit the daily activity radius of older adults, reduce social participation, and exacerbate health risks, thereby contradicting the democratic and inclusive principles of public space outlined in the “right to the city” theory [4] and exposing a structural deficiency in the aging-friendly design of current mountainous community parks. While Universal Design focuses on age-inclusive accessibility [5], it does not adequately address the specific needs of older adults, such as physiological decline and heightened risk perception. Mountainous community parks—public green spaces in high-density cities with significant topographical variations—serve as essential venues for daily recreation, socialization, and health activities, particularly for older adults. As the primary setting for their daily activities, the aging-friendly design of these parks is crucial not only for individual well-being but also for achieving “healthy aging” and “livable cities”. In response, the World Health Organization (WHO) introduced the “age-friendly communities” framework in 2007, emphasizing spatial optimization to promote healthy aging [6]. The unique geographical and socioeconomic conditions of mountainous cities provide a distinct research context. This study aims to establish a scientific needs assessment system and explore key elements of aging-friendly development in mountainous community parks from the perspective of spatial justice, thereby enhancing the social well-being of older adults and advancing theoretical frameworks for aging adaptation.

Satisfaction assessment after usage is a critical basis for promoting healthy site operation and renewal. Various statistical methods, such as correlation analysis [7], multiple linear regression [8], and geographically weighted regression [9], have been extensively employed in satisfaction studies. However, the impacts are inherently complex and nonlinear [10], and the simple linear assumptions in the aforementioned methods fail to fully capture the breadth of these influences [11,12]. Nonlinear models offer distinct advantages in representing these nonlinear relationships [13] and can yield valuable insights into relative importance and marginal effects [14]. Consequently, many researchers have shifted towards nonlinear models to more accurately capture the intricate relationships between dependent and independent variables. Common nonlinear models include the multinomial logit (MNL), ordered logit, and ordered probit models, among others, which have been widely applied in numerous studies [13,15,16]. However, while substantial attention has been devoted to model development and parameter estimation, the performance of these models in evaluating their impacts has been largely neglected, leaving the question of the most appropriate method unanswered.

In the field of age-friendly design for community parks, international research has established a relatively systematic theoretical framework and practical paradigm. Nordic countries optimize park walking networks based on the Universal Accessibility principle, integrating barrier-free facilities to enhance the spatial autonomy of older adults [17]. Tokyo’s “Health Park” model fosters the physiological–psychological coordination of older adults by spatially coupling age-friendly exercise facilities with social nodes [18]. Research in North America from an environmental psychology perspective confirms the positive role of green spaces in cognitive maintenance and emotional regulation [19]. However, existing studies primarily focus on flat or mildly hilly urban areas, emphasizing facility adaptability, social interaction, and environmental healing functions, limiting their applicability to mountainous cities. In these cities, steep terrain (average slope > 15%), spatial fragmentation, and complex vertical transportation restrict the mobility of older adults, exacerbating challenges in facility accessibility and usage efficiency [20]. Although some studies have identified key factors influencing older adults’ spatial satisfaction [21], the development of an age-friendly park planning system for this specific topographical context remains underexplored. Thus, it is essential to further investigate the impact of mountainous environments on walking accessibility, facility adaptability, and spatial connectivity to inform more targeted age-friendly design strategies.

In high-density urban areas, dense clusters of buildings create significant psychological stress for residents [22], which notably increases the likelihood of mental and physical health issues, such as depression and cardiovascular diseases, especially among older adults [23]. Therefore, it is critical to investigate how the design of community parks can alleviate this psychological stress, reduce loneliness among older adults, and foster a positive and inviting park environment.

This study explores the influence of various planning factors in community parks on older adults’ satisfaction in high-density mountainous cities. Specifically, it addresses the following three research questions:

(1)

Which regression model best captures the nonlinear variations in older adults’ satisfaction?

(2)

Which planning factors have the most significant impact on older adults’ satisfaction in these parks, and what is their relative importance?

(3)

How can community park construction mitigate psychological stress and loneliness in older adults and promote a positive park atmosphere?

To address these questions, this study will gather usage data from typical high-density community parks in Chongqing through field visits and surveys. Principal component analysis will be employed to identify key factors influencing older adults’ satisfaction, and the performance of various regression models will be compared. The most appropriate model will then be used to assess how different park planning factors impact older adults’ satisfaction. This research aims to inform age-friendly design in community parks within high-density mountainous urban settings and contribute to the development of more livable cities.

2. Methodology

2.1. Study Area

Chongqing, one of China’s four direct-controlled municipalities, has a population exceeding 32 million. As a typical high-density mountainous city, approximately 80% of its land area is characterized by hills and mountains, with slopes greater than 8° covering 85.51% of the terrain [24]. The city experiences a subtropical monsoon climate, marked by hot, humid summers and mild, damp winters [25]. Considering Chongqing’s urban morphology and its aging population, this study selected three districts—Jiulongpo, Nan’an, and Yubei—as sample park sites. First, all three districts display typical mountainous urban characteristics, with average altitudes ranging from 200 to 500 m and maximum elevation differences exceeding 500 m [26]. Second, the proportion of older adults (18.2–21.5%) in these areas is significantly higher than the citywide average (17.6%), and the population density exceeds 12,000 people per square kilometer [3], resulting in a substantial supply–demand imbalance in public space.

Based on field research conducted from 27 to 30 April 2024, three parks in urban renewal areas were selected for study (

Table 1. Overview of park physical environment and activity organization types.

	Yugao Park	Nanhu Community Shuangyong Cultural Park	Wanqing Park
Spatial Connectivity	***	*	*
Area (hm2)	5.00	1.31	0.96
Accessibility	***	*	**
Proximity to bus stops/metro stations	√	×	×
Surrounding Amenities	***	*	**
Park Infrastructure Richness	***	*	**
Architectural Shading Structures	√	√	√
Square Suitable for group activities	√	×	√
Pavilion	√	√	√
Independent exercise and fitness area	√	×	×
Toilet	√	√	√
Abundant recreational seating	√	√	√
Park safety and maintenance	***	*	**
Landscape environment	***	*	***
Greening	***	***	***
Water features	√	×	√
Landscape cultural elements	*	***	**
Types of activities for the elderly	Recreational sitting, Tai Chi, square dancing, childcare, socializing, badminton, table tennis, walking and jogging, elderly public services.	Walking, child care, dog walking, socializing and resting, sitting and meditating.	Playing instruments, walking for leisure, sitting quietly for observation, playing chess, socializing, babysitting, and exercising.

Note: *** indicates very good, ** indicates average, * indicates poor; “√” indicates present, “×” indicates absent.

, Figure 1). Yugaogong Park (5 hectares) has a vertical elevation difference of up to 30 m and a maximum slope of 15%, incorporating age-friendly features such as fitness trails. Nanhu Shuangyong Park (1.31 hectares) creates pedestrian activity spaces through terrain with slopes ranging from 5% to 15%. Wanjing Park (0.96 hectares) takes advantage of a 10–30 m elevation difference to create natural activity interfaces. All three parks are situated in older communities with buildings over 15 years old, where more than 20% of residents are aged 60 and above. Field observations indicate that over 65% of park users are older adults. The spatial configurations of these parks include fitness trails, barrier-free facilities, rest nodes, and cultural amenities, supporting multifunctional activities such as walking, fitness, social interaction, and childcare (Figure 2).

2.2. Questionnaire Design

The questionnaire developed for this study was based on a systematic review of the literature concerning the impact of community park planning factors on older adults’ satisfaction. Its purpose is to establish a comprehensive survey framework consisting of 46 distinct items that influence satisfaction. Of these, 28 items address environmental characteristics, while 18 items focus on social attributes. The questionnaire development was informed by existing research, which identified key planning factors, including spatial connectivity [27], accessibility, convenience of public transportation [28], barrier-free facilities [29], landscape quality [30], infrastructure functionality and safety [31], social participation, social spaces, and opportunities for interaction [32,33], as well as regional cultural integration and emotional resonance [28,34]. Based on this literature review, this study identified 46 potential planning factors (Appendix A).

Determination of Questionnaire Planning Factors Based on the Delphi Method

The Delphi Method, a well-established group decision-making approach [35], utilizes an anonymous, multi-round questionnaire survey system with iterative feedback mechanisms to effectively integrate independent judgments and expert insights, leading to a statistically significant group consensus. Unlike traditional decision-making methods, the Delphi Method mitigates common issues such as authority and conformity biases through a structured procedural control. Its feedback process preserves the independence of expert opinions while optimizing predictive outcomes by gradually converging divergent views [36].

In this study, a consulting group composed of 11 interdisciplinary experts from urban planning, landscape design, architecture, and geriatric psychology was formed. The Delphi Method, combined with a 5-point Likert scale (1 = not important at all, 5 = extremely important), was employed to develop an indicator system. After two rounds of iterative evaluation, the indicators were selected and validated. As shown in

Table 2. Development and validation of indicators.

Steps	Number of Items Assessed and Retained	Number of Participants	Response Rate	Examples of Discard and Merge Indicators	Kendall Factor
Round 1	46 indicators were sent to participants and 38 indicators with an average score greater than 3.5 were retained.	11 people	90.9%	Remove indicators for scenic rest areas, volunteer space, etc.	0.490
Round 2	38 indicators were sent to participants and 33 were retained for this round.	10 people	100%	Accessibility to public transportation and frequency of public transportation were merged and three indicators for neighborhood services were merged into one indicator, etc.	0.561

, the study strictly adhered to the standardized Delphi process, systematically outlining the entire development process from the initial drafting of indicators to the establishment of the system.

This study developed an indicator system through two rounds of expert consultations. The first round involved 11 experts from the field (Appendix B), with 10 valid responses received (response rate: 90.9%). After expert evaluation, indicators such as “scenic area rest zones” and “volunteer service spaces”, which failed to meet the screening criteria (removal threshold: average score < 3.5), were excluded, leaving 38 indicators (M ≥ 3.5) [37]. In the second round, 10 experts participated, achieving a 100% response rate. Through dimension integration, the initial indicators were refined: “public transport convenience” and “public transport frequency” were consolidated into “public transport accessibility”, and the three indicators related to surrounding service facilities were merged into one. Following two rounds of iterative optimization, the final evaluation system comprised 33 core indicators. The expert consensus test yielded a Kendall’s W coefficient of 0.561 (p < 0.01), indicating a high level of agreement among the experts.

The questionnaire was designed with a focus on communication with older adults, aiming to comprehensively assess how community park planning factors influence their psychological needs [38]. It is divided into two main sections: the first section collects demographic data, including age, gender, education level, income, and length of residence. The second section evaluates respondents’ satisfaction with community park planning factors using a 5-point Likert scale (Appendix C).

2.3. Data Collection

Data collection primarily employed a face-to-face stratified random-sampling approach, targeting older adults aged 60 and above in three parks. Survey participants were regular park users, which ensured the validity of the collected data. A total of 358 valid questionnaires were obtained, with 123 from Yugao Park, 116 from Nanhu Community Shuangyong Cultural Park, and 119 from Wanqing Park.

2.4. Data Analysis

2.4.1. Principal Component Analysis

After completing the questionnaire survey, we applied principal component analysis (PCA) to reduce the dimensionality of the thematic data. PCA is a multivariate statistical technique that employs orthogonal linear transformations to convert a set of correlated variables into a smaller number of uncorrelated variables (i.e., principal components, PCs). The first principal component (PC) captures the maximum variance and represents the largest contribution to the data, followed by the second PC, third PC, and so on. By doing so, PCA minimizes collinearity among predictor variables. Data analysis was performed using SPSS 27.0. The PCA calculation equation is as follows:

$$P{C}_i=I_{i1}{X}_1+I_{i2}{X}_2+\cdots +I_{in}{X}_n$$

$P{C}_i$ represents the $i$-th principal component, $I_{ij}$ denotes the principal component coefficient vector, and $X_j$ is the $j$-th predictor variable ($i$, $j$ = 1,2,…, $n$) [39].

2.4.2. Model Selection

Before conducting the analysis, we evaluated the applicability of commonly used models. A review of the literature indicates that satisfaction among older adults is an ordinal categorical variable (e.g., ranging from “very dissatisfied” to “very satisfied”). Traditional linear regression models, which assume a linear relationship and normally distributed errors, often lead to biased parameter estimates [40]. In contrast, nonlinear models construct probability distributions through latent variables, making them more suitable for analyzing ordinal dependent variables [41]. In mountainous cities, the relationship between planning factors (e.g., accessibility, topographical variations) and satisfaction often exhibits threshold effects or interactions. Nonlinear models are better suited to capturing these complex associations [42]. Compared to machine learning approaches (e.g., random forests, neural networks), nonlinear regression models offer interpretable coefficients and marginal effects, enabling a direct quantification of variable influences and providing a clearer basis for planning decisions [13]. Therefore, this study employs nonlinear regression models for subsequent analysis.

2.4.3. Comparison of Regression Models

Three regression models—the ordered probit model, the multinomial logit model, and the ordered logit model—were applied to examine the nonlinear effects of community park planning on elderly satisfaction. All three models fall under the category of discrete choice models [13].

• Ordered Probit Model

The model first converts the continuous latent variable into the probability of ordered categorical dependent variables using the cumulative distribution function of the normal distribution. The model parameters are then estimated through the maximum likelihood estimation method. The calculation formula for the ordered probit model is as follows:

$$Y^{\mathrm{*}}=X\beta +ϵ$$

Here, $Y^{\mathrm{*}}$ represents the unobservable latent variable, $X$ is the matrix of explanatory variables, $\beta$ is the coefficient vector, and $ϵ$ is the error term, where $ϵ$ follows a standard normal distribution. The relationship between the observed ordered response variable $Y$ and the latent variable $Y^{\mathrm{*}}$ is as follows:

$$Y=j \mathrm{if} {\tau }_{j-1}<Y^{\mathrm{*}}\le {\tau }_j$$

Here, ${\tau }_j$ is the threshold parameter, where $j$ = 1, 2, …, $j$.

Marginal Effect Formula: The calculation of marginal effects in an ordered probit model is relatively complex as it depends on the threshold parameters. The marginal effect of an explanatory variable $X_k$ can be expressed as follows:

$$\begin{array}{c}{\displaystyle \frac{\partial Pr(Y=j|X)}{\partial X_k}}=\mathrm{\Phi }({\tau }_j-X\beta )-\mathrm{\Phi }({\tau }_{j-1}-X\beta )\end{array}$$

where $\mathrm{\Phi }$ is the cumulative distribution function of the standard normal distribution [43].

b.

Multinomial Logit Model

The multinomial logit model is used to estimate the probability of each categorical outcome from more than two discrete choices, where the log-odds of the outcomes are represented as a linear combination of predictor variables. Its basic form is as follows:

$$\mathrm{l}\mathrm{n}\left({\displaystyle \frac{P(Y=i|X)}{\overline{P(Y=J|X)}}}\right)=X{\beta }_i$$

Here, $P(Y=i|X)$ represents the probability of the response variable $Y$ falling into the $i$-th category given the explanatory variables $X$. ${\beta }_i$ is the coefficient vector for the $i$-th category, and $J$ denotes the reference category.

Marginal Effect Formula: The marginal effect of the explanatory variable $X_k$ can be expressed as follows:

$${\displaystyle \frac{\partial P(Y=i|X)}{\partial X_k}}=P\left(Y=i|X\right)\times \left(1-P\left(Y=i|X\right)\right)\times {\beta }_{ik}$$

Here, ${\beta }_{ik}$ is the coefficient of the explanatory variable $X_k$ in the $i$-th category [44].

c.

Ordered Logit Model

The ordered logit model transforms continuous latent variables into the probabilities of ordered categorical dependent variables using the cumulative distribution function of the logistic distribution. The formula for the ordered logit model is as follows:

$$\ln \left({\displaystyle \frac{P\left(Y\le j|X\right)}{1-P\left(Y\le j|X\right)}}\right)=X{\beta }_j+{\alpha }_j$$

Here, $P\left(Y\le j|X\right)$ represents the probability that the response variable $Y$ is less than or equal to the $j$-th category, given the explanatory variable $X$. ${\beta }_j$ is the coefficient vector for the $j$-th category, and ${\alpha }_j$ is the threshold parameter.

Marginal Effect Formula: The marginal effect of the explanatory variable $X_k$ can be expressed as follows:

$${\displaystyle \frac{\partial P(Y=j|X)}{\partial X_k}}={\displaystyle \frac{\mathrm{e}\mathrm{x}\mathrm{p}(X{\beta }_j+{\alpha }_j)}{(1+\mathrm{e}\mathrm{x}\mathrm{p}(X{\beta }_j+{\alpha }_j){)}^2}}\cdot {\beta }_{jk}$$

where ${\beta }_{jk}$ is the coefficient of the explanatory variable $X_k$ in the $j$-th category.

In this study, community park planning factors and elderly satisfaction are treated as independent and dependent variables, respectively. Before applying the regression models, the data collected from the questionnaire were used to evaluate the performance of model fit and computational efficiency using indicators such as −2log(Λ), Pseudo R², p-value, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and iteration count. These metrics are employed to estimate the dependent variable using a test dataset, as outlined below (

Table 3. Model fit indicators.

Indicator	Description	Model	Formula
log(Λ)	A function that measures the goodness-of-fit between model parameters and data.	Ordered probit model	$\begin{array}{r}L\left(\beta ,\gamma |X,Y\right)=\prod _{i=1}^n\left[\mathrm{\Phi }\left({\gamma }_{Y_i}-X_i\mathrm{\prime }\beta \right)-\mathrm{\Phi }\left({\gamma }_{Y_i-1}-X_i\mathrm{\prime }\beta \right)\right]\end{array}$
		Multinomial logit model	$L\left(\beta |X,Y\right)=\prod _{i=1}^n\prod _{j=1}^J{\left({\pi }_{ij}\right)}^{\mathbb{I}\left(y_i=j\right)}$
		Ordered logit model	$L\left(\beta |X,Y\right)=\prod _{i=1}^n\left(\prod _{j=1}^{J-1}{\left({\displaystyle \frac{\mathrm{e}\mathrm{x}\mathrm{p}\left(X_i\mathrm{\prime }\beta \right)}{1+\mathrm{e}\mathrm{x}\mathrm{p}\left(X_i\mathrm{\prime }\beta \right)}}\right)}^{\mathbb{I}\left(y_i=j\right)}\right)$
Pseudo R2	An indicator used to measure the goodness-of-fit of statistical models, particularly in regression models, to assess the proportion of variance explained by the model.	Ordered probit model	$R_M^2=1-{\displaystyle \frac{ln\left(L\left(\widehat{\beta }\right)\right)}{ln\left(L\left(0\right)\right)}}$
		Multinomial logit model
		Ordered logit model
p	Used to assess the significance of model parameters.	Ordered probit model	$z=\left(\beta -{\beta }_0\right)/SE\left(\beta \right)$ $p=2^{\star }\Phi \left(-\left|z\right|\right)$
		Multinomial logit model
		Ordered logit model
AIC	AIC (Akaike Information Criterion) is a criterion used for model selection. It assesses the goodness-of-fit of the model while taking into account its complexity.	Ordered probit model	$AIC=-2\cdot ln\left(L\right)+2k$
		Multinomial logit model
		Ordered logit model
BIC	BIC (Bayesian Information Criterion) is another criterion for model selection, similar to AIC, but with a stricter penalty for model complexity.	Ordered probit model	$\mathrm{BIC}=-2\cdot \ln \left(L\right)+k\cdot ln\left(n\right)$
		Multinomial logit model
		Ordered logit model

).

3. Results

3.1. Principal Component Analysis Results

The PCA yielded consistent results, including eigenvalues, the percentage of variance explained, and the loadings of each principal component. The analysis was validated with a KMO value of 0.852, exceeding the threshold of 0.7, and passed Bartlett’s test (p < 0.001). The first six principal components, with eigenvalues greater than 1, collectively explained approximately 82.451% of the total variance (

Table 4. Results of principal component analysis.

Component	Sum of Squares of Rotational Loads
	Total	% of Variance	Cumulative %
1	8.702	26.370	26.370
2	5.531	16.760	43.130
3	4.033	12.223	55.353
4	3.569	10.815	66.168
5	3.190	9.668	75.836
6	2.183	6.615	82.451

, Figure 3), demonstrating that these components provide a robust representation of older adults’ overall satisfaction.

Based on the rotated component matrix, the first principal component (variance contribution of 26.37%) primarily encompasses five dimensions: spatial creation, sense of security, activities and fitness, social connections, and mobility. This component is referred to as “Park Spatial Activities and Social Connections (AS)”. The second component (variance contribution of 16.76%) includes five dimensions: accessibility, transportation convenience, public transport services, navigation and signage, and surrounding service facilities. We define it as “Park Accessibility and Surrounding Service Convenience (AC)”. The third component (variance contribution of 12.22%) consists of five dimensions: scenic views and shading, seasonal changes, natural connection, environmental maintenance, and landscape quality. We summarize it as “Landscape Environment and Natural Connection (EN)”. The fourth component (variance contribution of 10.82%) mainly involves four dimensions: infrastructure, comfort, accessibility and convenience, and management and cleanliness. This is defined as “Facility Maintenance and Accessibility Design (FB)”. The fifth component (variance contribution of 9.67%) contains two dimensions: respect and self-worth realization. This component is referred to as “Community Participation and Value Realization (PV)”. The sixth component (variance contribution of 6.62%) includes four dimensions: spiritual life, sense of belonging, cultural heritage, and intergenerational interaction. These are summarized as “Social and Cultural Exchange and Sense of Belonging (IS)”. Based on these components, the first six principal components (with a cumulative variance contribution of 82.45%) were extracted to construct predictive variables for subsequent analysis (Figure 4).

3.2. Model Performance

Based on raw data from three parks, we employed three regression models—ordered probit, multinomial logit, and ordered logit—using Stata MP 18.0. Model evaluation was conducted with indicators including −2log(Λ), Pseudo R², p-value, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Iteration Count. Among these, −2log(Λ), Pseudo R², p-value, AIC, and BIC were used to assess model fit. As shown in

Table 5. Measurement results of test indicators for all estimated models.

Model	−2log(Λ)	Pseudo R2	df	p	AIC	BIC	Iteration Count
Ordered probit model	1032.656	0.0743	6	0.000	1079.655	1118.516	4
Multinomial logit model	1059.655	0.0735	24	0.000	1087.78	1196.589	4
Ordered logit model	1031.778	0.0978	10	0.000	1078.656	1117.517	3

, the ordered logit model outperformed the other two across multiple indicators, including −2log(Λ) (1059.655), Pseudo R² (0.0978), p-value (0.000), AIC (1078.656), and BIC (1117.517). This indicates that the ordered logit model provides a more accurate representation of the data and is better suited for explaining the variables. The iteration count was used to evaluate computational efficiency, and the results showed that the ordered logit model converged in just three iterations, demonstrating its high efficiency. Consequently, the ordered logit model will be adopted in subsequent research to estimate the effects of predictor variables on the response variable [13].

3.3. Ordered Logit Model Estimation Results: Satisfaction Index and Marginal Effects

The predictive variables derived from principal component analysis were analyzed using ordered logit regression in Stata MP 18.0, with their marginal effects estimated in the R environment.

Table 6. Satisfaction index.

	Full Sample	Yugao Park	Nanhu Community Double Support Culture Park	Wanqing Park
(AS) Park spatial activities and social connections	0.4102298 *** (4.14)	1.400286 *** (3.88)	0.9813807 *** (2.81)	1.199866 *** (3.44)
(AC) Park accessibility and convenience of surrounding services	0.3939775 *** (4.06)	−0.3466703 (−0.89)	0.4589729 * (1.36)	1.012783 ** (2.56)
(EN) Landscape environment and connection to nature	0.3657768 *** (3.70)	−0.0951912 (−0.37)	1.643789 *** (5.56)	1.365491 *** (4.87)
(FB) Facility maintenance and barrier-free design	0.4582868 *** (4.61)	0.139908 (0.83)	1.268035 *** (5.87)	−0.0659899 (−0.38)
(PV) Community participation and value realization	0.3201275 *** (3.32)	0.0344181 (0.14)	−0.1024155 (−0.41)	−0.0732571 (−0.29)
(SB) Social cultural exchange and sense of belonging	0.3293253 *** (3.31)	1.041469 *** (5.7)	0.1842745 (0.93)	0.0290879 (0.17)
Pseudo R2	0.0978	0.1847	0.2133	0.1601
Prob > chi2	0.0000	0.0000	0.0000	0.0000
Log likelihood	−529.8276	−156.86219	−144.22333	−158.97591

Note: The numbers in parentheses represent z-statistics; * indicates statistical significance at the 10% level, ** at the 5% level, and *** at the 1% level.

and Figure 5 illustrate the distribution of the coefficients (β) for each predictor variable across the full sample and within three distinct parks. Based on the regression analysis, the marginal effects were further examined to evaluate the impact of planning factors on satisfaction levels across different categories. Figure 6, Figure 7, Figure 8 and Figure 9 depict the marginal effects of landscape planning factors for each park. The marginal effect of each factor quantifies the change in elderly users’ satisfaction levels associated with a one-unit increase in the factor. The findings highlight variations in satisfaction indices and their statistical significance across parks in multiple dimensions.

The distribution of coefficients and odds ratios for the full sample (Table 6, Figure 5) demonstrates that all six planning factors exert significant effects, ranked in descending order of impact strength as follows: FB > AS > AC > EN > SB > PV. Notable differences exist in satisfaction indices across various community park planning factors. Predictive analysis based on marginal effects further confirms the varying influence of different park planning and design elements. Overall, facility accessibility, spatial social connections, general accessibility, and landscape environment emerge as the primary determinants of older adults’ satisfaction. The marginal effect analysis for the full sample indicates that all six factors significantly and positively contribute to satisfaction, with each unit increase in an independent variable corresponding to a proportional rise in overall satisfaction levels. These findings suggest that, in high-density mountainous urban parks, the provision of accessible facilities, social and spatial connectivity, and a well-designed landscape environment universally enhances older adults’ satisfaction. Specifically, Yugao Park places greater emphasis on spatial activities and social interactions, while Nanhu Community Shuangyong Cultural Park exhibits a stronger influence of accessible facilities and landscape environment. Meanwhile, in Wanqing Park, improvements in accessibility, given the substantial topographical variations, have markedly enhanced satisfaction levels.

For the full sample, the calculated satisfaction indices reveal that “Facility Maintenance and Accessibility Design” (FB) exerts the most significant influence on satisfaction (β = 0.458). Given the considerable elevation differences in Nanhu Community Shuangyong Cultural Park, marginal effect analysis highlights FB’s pronounced impact on satisfaction, increasing the probabilities of “satisfied” and “very satisfied” by 10.9% and 6.9%, respectively. This effect is attributable to the mobility constraints imposed by large elevation variations in mountainous cities, which limit older adults’ range of activities. Enhancing facility maintenance and accessibility design can significantly expand their mobility and opportunities for social interaction, thereby improving overall park satisfaction.

With accelerating urbanization and spatial constraints imposed by mountainous topography, land use in these cities has become increasingly restricted. Community parks serve as essential spaces for physical activity and social interaction, particularly for older adults in high-density urban environments. Empirical results indicate that “Spatial Activities and Social Connections” (AS) positively influence satisfaction across the full sample and all three independent samples, passing the 5% significance level test. This effect likely stems from the constrained daily activity radius of older adults in high-density mountainous cities, where community parks often constitute the only accessible social space. These findings underscore the importance of incorporating additional social spaces into future park designs to better accommodate the needs of older adults.

Accessibility (AC) is another critical factor shaping older adults’ satisfaction with community parks. This study identifies a significant positive correlation between accessibility and satisfaction, with the relationship passing the 5% significance level test in the full sample. Compared to other parks, Wanqing Park, characterized by pronounced topographical fluctuations and limited transportation convenience, exhibits a more pronounced effect of AC. Specifically, each unit increase in AC corresponds to an 11.8% rise in satisfaction, highlighting the necessity of prioritizing accessibility in the planning of community parks in high-density mountainous cities.

The landscape environment (EN) also plays a pivotal role in shaping older adults’ satisfaction with community parks. Rich greenery and vegetation, as fundamental natural elements, foster a comfortable and pleasant leisure environment, significantly enhancing quality of life and livability [45]. Empirical findings indicate that EN has a positive effect on satisfaction in the full sample, as well as in Nanhu Park and Wanqing Park, with all passing the 5% significance test. However, in Yugao Park, EN does not exhibit a significant effect, likely due to the park’s extensive area, diverse vegetation, and varied spatial configurations, which already provide a high-quality landscape environment, making further improvements less perceptible to older adults.

Finally, while the effects of “Social and Cultural Exchange and Sense of Belonging” (SB) and “Community Engagement and Value Fulfillment” (PV) are comparatively minor, their optimization remains essential once basic infrastructure and activity spaces are secured. Studies indicate that when well-established facilities and accessibility are in place, older adults tend to prioritize social interaction and cultural participation [46]. Thus, SB and PV should not be overlooked, particularly in the context of contemporary urban development goals that emphasize high-quality growth.

In conclusion, this study underscores that facility maintenance and accessibility design (FB), spatial activities and social connections (AS), accessibility (AC), and landscape environment (EN) are the primary determinants of older adults’ satisfaction, though their relative influence varies across different parks. In mountainous urban environments, special attention should be given to accessibility and accessibility design, which are crucial for older adults’ mobility, sense of security, and social participation. These findings highlight the need for future park designs to not only optimize infrastructure but also integrate social interaction spaces and natural environments, thereby holistically enhancing older adults’ quality of life and well-being.

4. Discussion

4.1. The Applicability of the Ordered Logit Model

The intricate landscapes, dense environments, and multidimensional planning factors of mountainous cities often lead to a nonlinear relationship between satisfaction and planning variables. In this context, traditional linear regression and binary logit models frequently fail to capture these complex interactions and the ordinal nature of the data. Since satisfaction is an ordinal variable (e.g., ranging from “very dissatisfied” to “very satisfied”), conventional linear models, which assume linear relationships, may introduce bias when analyzing such data [40]. To address this issue, this study evaluates three commonly used nonlinear models—ordered probit, multinomial Logit (MNL), and ordered logit—by comparing their goodness-of-fit and computational efficiency. The results demonstrate that the ordered logit model is the most effective in handling ordinal data and nonlinear relationships, outperforming the other models. Although its Pseudo R² is relatively low due to sample size constraints and the unique topography of mountainous cities, it remains within an acceptable range for similar studies [45]. Furthermore, the marginal effects analysis provides valuable insights, revealing that enhancing accessibility facilities increases the likelihood of “satisfaction” by 10.9%. This finding aligns with Greene [41], who underscores the ordered logit model’s superior performance in analyzing ordinal dependent variables.

Additionally, by leveraging the marginal effects analysis of the ordered logit model, this study further confirms its applicability in assessing urban park planning in high-density mountainous cities. The analysis offers clearer insights into how various planning factors influence older adults’ satisfaction, thereby providing precise decision-making support for park planners. As Freese [47] noted, the ordered logit model’s marginal effects comprehensively illustrate how changes in independent variables alter the probability distribution of satisfaction levels, offering a more holistic perspective on the complexities of urban park planning.

4.2. Key Factors in the Construction of Age-Friendly Community Parks

Through principal component analysis, six core factors were identified, forming the foundation for examining the factors influencing satisfaction. By combining the ordered logit model with marginal effect analysis, the results reveal that all six factors significantly and positively affect satisfaction, with the strength of influence ranked as follows: FB > AS > AC > EN > SB > PV. Key factors influencing older adults’ satisfaction include accessibility features, spatial and social connections, accessibility, and the landscape environment, with accessibility features having the most significant impact. Specifically, for each unit increase in accessibility features, the likelihood of older adults selecting “satisfied” and “very satisfied” increases by 10.9% and 6.9%, respectively. This result aligns with findings from Kaczynski, Besenyi, Stanis, Koohsari, Oestman, Bergstrom, Potwarka and Reis [48]. As accessibility improves, older adults’ satisfaction with community parks also increases. In mountainous cities, the challenges posed by complex terrain—such as travel inconvenience and facility adaptability—make accessibility features and overall accessibility key factors for enhancing older adults’ satisfaction [45,49]. This phenomenon can be attributed to the terrain’s impact on the demand for transport convenience and public service accessibility [50]. Mountainous cities often face issues like insufficient public transportation and complex walking paths due to significant elevation differences and rugged roads, which exacerbate the negative impact of travel barriers on older adults’ daily lives. According to Hayauchi, Ariyoshi, Morikawa and Nakamura [20], every 1 m increase in vertical height for physical activity is equivalent to walking 9.54 m on flat ground. This not only limits older adults’ mobility but may also restrict their participation in social activities, thereby significantly reducing their satisfaction [51]. In contrast, in flat cities, where terrain has less impact and facility connectivity is higher, improvements in older adults’ satisfaction are more dependent on factors such as landscape quality and functional optimization. Thus, enhancing the coverage of accessibility features and improving community accessibility is particularly critical for elevating the quality of life for older adults in mountainous cities.

4.3. The Dynamic Mechanism of Psychological Needs on Satisfaction

The results of this study indicate that the overall impact of “socio-cultural interaction and sense of belonging” (SB) is relatively low. However, as the overall quality and supporting facilities of community parks continue to improve, the psychological needs of older adults may become a more significant factor influencing their satisfaction with park use [46]. The results from Yugao Park, which has superior facilities, reveal a higher impact of SB on satisfaction. Further evidence suggests that when older adults experience psychological needs related to leisure activities, those with fewer perceived activity limitations tend to participate more, resulting in higher satisfaction during park visits [52]. This implies that, with the improvement of park infrastructure, psychological needs may become a key factor in enhancing older adults’ satisfaction with parks. Future studies should further explore the psychological needs of older adults in relation to park use. Additionally, Afshar, Foroughan, Vedadhir and Tabatabaei [53], Han, Li and Chang [33], and Chen, Sun and Seo [54] found a significant positive correlation between place attachment and older adults’ well-being. Neighborhood communities provide a social support network where older adults can establish friendships and mutual support relationships, enhancing their sense of security and providing assistance when needed. As attachment to place strengthens, older adults exhibit greater self-control, a stronger sense of social identity, and closer interactions with community residents, ultimately reducing loneliness [55,56]. This research offers valuable cultural insights into park planning and management, emphasizing the importance of addressing the psychological needs and sense of participation among older adults.

Currently, most older adults are not involved in the park planning decision-making process. This study indicates that “community participation and value realization” (PV) did not show significant impacts across three independent parks, likely due to limited opportunities for older adults to engage in the planning process or the absence of mechanisms to incorporate their specific needs and preferences into decision-making. This reflects the lack of participation in park management. To address this issue, Washington, Cushing, Mackenzie, Buys and Trost [57] suggested that fostering older adults’ participation through collaborative park maintenance and decision-making could strengthen their sense of belonging to the park, thereby enhancing their well-being and satisfaction.

Moreover, cultural differences must also be considered. Unlike Western cultures, an important aspect of older adults’ park participation in China involves childcare. This is not only a critical part of their daily activities but also a key source of social engagement. Therefore, child-friendliness should be a fundamental consideration in park planning. As a multi-generational social space, parks foster intergenerational interactions and cultural transmission, fulfilling an essential social function [57].

4.4. Limitations and Future Research Directions

This study proposes a novel theoretical framework for designing age-friendly community parks using nonlinear models, particularly within the context of high-density mountainous cities, thereby addressing a critical gap in existing research. The findings offer valuable policy insights for age-friendly urban design, such as optimizing ramp gradients to enhance spatial inclusivity and increasing the distribution of rest areas tailored to older adults. However, this study has certain limitations. It does not provide detailed case studies illustrating how age-friendly design can be implemented across varying topographical conditions. Furthermore, the sample is restricted to three community parks in Chongqing, without fully accounting for the impact of financial constraints, policy support, and community participation on the practical implementation of age-friendly design. Future research should encompass a broader range of cities and investigate the potential of emerging technologies, such as intelligent monitoring and virtual simulation, to improve the design and management of age-friendly parks. Through the analysis of the three parks, we found that accessibility enhancements and landscape improvements significantly influence older adults’ satisfaction. However, variations in park topography and surrounding environments lead to differences in satisfaction levels. Future studies should integrate perspectives from psychology and sociology to further explore the impact of older adults’ psychological needs and social interactions on park satisfaction.

5. Conclusions

In this study, we selected three community parks characterized by mountainous, high-density environments in central Chongqing as case studies. A total of 358 valid questionnaires were collected, and principal component analysis (PCA) was employed to identify key planning factors. We then utilized an ordered logit model and marginal effect analysis to assess the impact of these factors on older adults’ satisfaction. The key findings are as follows:

The ordered logit model effectively captures complex nonlinear relationships in evaluating community park planning within mountainous high-density urban areas, particularly regarding older adults’ satisfaction (−2log(Λ) = 1059.655, Pseudo R² = 0.0978, p = 0.000, AIC = 1078.656, BIC = 1117.517). Due to its superior computational efficiency, this model outperforms traditional linear regression and other commonly used nonlinear models, making it a more effective analytical tool.

All six key factors identified through PCA exhibit significant positive effects on older adults’ satisfaction, ranked in order of influence as FB > AS > AC > EN > SB > PV. Among them, accessibility facilities (FB), spatial and social connectivity (AS), accessibility (AC), and landscape environment (EN) are the primary determinants, with satisfaction indices exceeding 0.35. Accessibility facilities have the strongest impact, with a coefficient of 0.458, highlighting the critical role of facility accessibility and barrier-free design in enhancing the quality of life for older adults in mountainous cities.

The psychological needs of older adults also exert a dynamic influence on satisfaction. When infrastructure is underdeveloped, demand for SB and PV remains low, but as infrastructure improves, this demand increases. This suggests that parks should not only fulfill functional needs but also enhance visitation motivation, foster a sense of belonging, and provide spaces for social interaction. Such improvements can promote intergenerational integration and strengthen community vitality.

This study innovatively reveals the nonlinear effects of planning elements in age-friendly community parks on older adults’ satisfaction in high-density mountainous cities, providing a quantitative decision-making framework for designing such parks under complex topographical conditions. Utilizing principal component analysis and an ordered logit model, the study quantifies older adults’ demand intensity for landscape maintenance, natural environments, and intergenerational spaces, highlighting their nonlinear effects. These findings offer a robust quantitative foundation for age-friendly park design in mountainous cities, aiding planners in developing adaptive strategies for community parks in high-density mountainous urban environments. As a mountainous country, China has over 40% of its cities situated in mountainous regions, with an even higher proportion in the southwest. Given their comparable development stages, spatial constraints, planning policies, and population densities, this study’s insights are highly relevant and valuable for similar urban contexts.