Method for judging traveler selection tendency through factor equilibrium model

Abstract

The invention provides a method for discriminating a traveler selection tendency by a factor equalization model, and relates to the technical field of traffic engineering, and the method comprises the following steps: collecting travel selection data of travelers, and obtaining a multi-dimensional data set through data arrangement; on the basis of the multi-dimensional data set, key factors influencing traveler decision making are extracted through a factor analysis method; according to the extracted key factors, constructing a factor equalization model by using a hybrid strategy, and solving the model to obtain an optimal travel strategy of the traveler; and according to the optimal travel strategy of the traveler, adjusting the delivery strategy of the vehicle. According to the method, the preference degree of individuals for different travel modes and the influence degree of factors such as gender, specialty and personal psychology on travel selection can be deeply known, so that important decision support is provided for optimizing urban traffic management and improving traffic efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic engineering, and in particular to a method for determining traveler's choice tendency using a factor equilibrium model. Background Art

[0002] The traditional method of judging the choice tendency of travelers is to use a logistic regression model, and the statistical data of the information is regressed and analyzed using a logistics model. This method ignores the influence of other factors such as personal subjective conditions and weather on the choice. In addition, in order to solve the shortcomings of the above model, a mixed model is introduced, that is, subjective feelings such as personal feelings and personality are used as a latent variable, measured through a structural equation model, and then the measured latent variable is listed with parameters such as personal gender, age, education, and income as one of the personal statistical information and participates in the logistics model.

[0003] At present, although the improved hybrid choice model can reflect the influence of personal subjective feelings on choice behavior, the underlying method is still a logical choice model. It has weak judgment ability for nonlinear factor analysis and relies on large data samples. In the case of insufficient information or other insufficient data, the traditional model has poor adaptability.

[0004] Currently, no effective solution has been proposed for the problems in the related technologies. Summary of the invention

[0005] In view of this, the present invention provides a method for identifying travelers' choice tendency using a factor equilibrium model to solve the above-mentioned problem.

[0006] In order to solve the above problems, the specific technical solutions adopted by the present invention are as follows:

[0007] A method for determining a traveler's choice tendency using a factor equilibrium model, the method comprising the following steps:

[0008] S1. Collect the travel choice data of travelers and obtain a multidimensional data set through data collation;

[0009] S2, based on multidimensional data sets, using factor analysis to extract key factors that affect travelers’ decisions;

[0010] S3. Based on the extracted key factors, a factor equilibrium model is constructed using a mixed strategy, and the optimal travel strategy of travelers is obtained through model solving;

[0011] S4. Adjust the deployment strategy of transportation vehicles based on the optimal travel strategy of travelers.

[0012] Preferably, the method of extracting key factors influencing travelers' decisions by factor analysis based on a multidimensional data set comprises the following steps:

[0013] S21, preprocessing the data variables in the multidimensional data set;

[0014] S22, constructing a factor model based on the preprocessed multidimensional data set;

[0015] S23. Based on the constructed factor model, the key factors that affect travelers’ decision-making are extracted by calculating the factor loading matrix.

[0016] Preferably, the preprocessing of the data variables in the multidimensional data set comprises the following steps:

[0017] S211, performing data cleaning processing on the data variables in the multidimensional data set, including processing of missing values ​​and outliers;

[0018] S212, performing standardization processing on the data variables in the multidimensional data set after data cleaning to obtain standardized data;

[0019] The mean value of each data variable in the standardized data is 0 and the variance is 1.

[0020] Preferably, the factor model is expressed as:

[0021] X = ΛF + u;

[0022] In the formula, X represents the data variable matrix;

[0023] A represents the loading matrix;

[0024] F represents the common factor;

[0025] u represents a special factor.

[0026] Preferably, the step of extracting key factors that affect travelers' decisions by calculating a factor loading matrix based on the constructed factor model comprises the following steps:

[0027] S231, calculating the covariance matrix of the data variables in the preprocessed multidimensional data set according to the preprocessed multidimensional data set;

[0028] S232, performing eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors;

[0029] S233. According to the size of the eigenvalue, select the eigenvectors corresponding to the first m largest eigenvalues ​​and form a factor loading matrix;

[0030] S234. Analyze the factor loading matrix and extract the key factors that affect travelers' decisions.

[0031] Preferably, the step of constructing a factor equilibrium model using a hybrid strategy based on the extracted key factors and solving the model to obtain the optimal travel strategy for travelers includes the following steps:

[0032] S31. Based on the extracted key factors, establish utility functions for different travel modes of travelers;

[0033] S32, establishing a mixed strategy, allowing travelers to choose between different travel modes with a pre-set probability, and calculating the expected utility of the travelers under the mixed strategy;

[0034] S33. Based on the expected utility of travelers under mixed strategies, a factor equilibrium model is constructed and solved to obtain the Nash equilibrium result;

[0035] S34. Analyze the Nash equilibrium results and obtain the optimal travel strategy for travelers.

[0036] Preferably, the utility function is expressed as:

[0037] U iA =α i +β 1i F 1i +β 2i F 2i +ε iA ;

[0038] Where U iA represents the utility function of traveler i choosing travel mode A;

[0039] α i represents a constant term;

[0040] β 1i , β 2i The coefficients of the common factors F1 and F2 representing the choice of travel mode A;

[0041] ε iA represents a random interference term.

[0042] Preferably, the hybrid strategy is established to allow travelers to choose between different travel modes with a preset probability, and the formation of the hybrid strategy space includes the following steps:

[0043] S321, determine the travel mode of the traveler and construct a travel choice set;

[0044] S322. For each traveler, according to the constructed travel choice set, determine the probability of the traveler choosing different travel modes based on the probability distribution;

[0045] S323, the travel choices of all travelers are combined to form a mixed strategy space;

[0046] S324. Calculate the expected utility of the traveler under the mixed strategy through the expected utility function.

[0047] Preferably, the expected utility function is expressed as:

[0048] E[U iA ]=p i U iA +(1-p i ) iB ;

[0049] In the formula, E[U iA ] represents the expected utility of traveler i under the mixed strategy;

[0050] p i represents the probability that traveler i chooses travel mode A;

[0051] U iA represents the utility function of traveler i choosing travel mode A;

[0052] U iB represents the utility function of traveler i choosing travel mode B;

[0053] 1-p i represents the probability that traveler i chooses travel mode B.

[0054] Preferably, the step of constructing and solving a factor equilibrium model based on the expected utility of the travelers under the mixed strategy to obtain a Nash equilibrium result comprises the following steps:

[0055] S331, establishing constraint conditions according to the expected utility of the traveler under the mixed strategy, and calculating the traveler's choice probability according to the traveler's utility function;

[0056] S332, taking the choice probability of maximizing the utility function of the traveler as the objective function;

[0057] S333, establishing a factor equilibrium model according to the constraint conditions and the objective function;

[0058] S334. Solve the factor equilibrium model to obtain the Nash equilibrium result.

[0059] The beneficial effects of the present invention are:

[0060] 1. The present invention utilizes the factor equilibrium model to explore the influence of various factors on individuals when choosing travel modes, so as to find the travel behavior strategy with the highest probability of participants, thereby providing a reference for the investment in corresponding means of transportation. The purpose of this model is to understand and explain the travel behavior of individuals under different selection conditions, and provide the probability distribution of the number of people choosing different travel modes, so as to provide a reference for formulating traffic policies or promoting new transportation modes. By analyzing the factor equilibrium model, we can deeply understand the individual's preference for different travel modes, as well as the influence of factors such as gender, profession, and personal psychology on travel choices, thereby providing important decision-making support for optimizing urban traffic management and improving traffic efficiency.

[0061] 2. The present invention adopts a mixed strategy modeling technology, which is involved in the factor equilibrium model. It obtains the load parameters for selecting different transportation modes from the factor analysis results, and participates in the solution of the mixed strategy Nash equilibrium model. At the same time, this is also a method of data dimensionality reduction analysis. It can analyze and select common latent variable data from a variety of data for dimensionality reduction, and then use probability distribution to analyze the overall situation to obtain the optimal response measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0063] Figure 1 The present invention is a flowchart of a method for determining a traveler's choice tendency using a factor equilibrium model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this application.

[0065] According to an embodiment of the present invention, a method for determining traveler selection tendency using a factor equilibrium model is provided.

[0066] The present invention is further described with reference to the accompanying drawings and specific embodiments. Figure 1As shown, according to the method for determining the traveler's choice tendency using a factor balance model according to an embodiment of the present invention, the method for determining the traveler's choice tendency using a factor balance model includes the following steps:

[0067] S1. Collect the travel choice data of travelers and obtain a multidimensional data set through data collation;

[0068] It should be noted that first, a large amount of data covering a wide range of variables that may affect the behavioral choices of individuals in specific decision-making situations should be collected. The data can come from questionnaires, behavioral records, social media, etc.

[0069] S2, based on multidimensional data sets, using factor analysis to extract key factors that affect travelers’ decisions;

[0070] As a preferred implementation, the method of extracting key factors influencing travelers' decisions based on a multidimensional data set using factor analysis includes the following steps:

[0071] S21, preprocessing the data variables in the multidimensional data set;

[0072] As a preferred implementation, the preprocessing of the data variables in the multidimensional data set comprises the following steps:

[0073] S2 11. Perform data cleaning on the data variables in the multidimensional data set, including the processing of missing values ​​and outliers;

[0074] S212, performing standardization processing on the data variables in the multidimensional data set after data cleaning to obtain standardized data;

[0075] The mean value of each data variable in the standardized data is 0 and the variance is 1.

[0076] S22, constructing a factor model based on the preprocessed multidimensional data set;

[0077] As a preferred implementation, the factor model is expressed as:

[0078] The expression of the factor model is:

[0079] X = ΛF + u;

[0080] In the formula, X represents the data variable matrix;

[0081] Λ represents the load matrix;

[0082] F represents the common factor;

[0083] u represents a special factor.

[0084] S23. Based on the constructed factor model, the key factors that affect travelers’ decision-making are extracted by calculating the factor loading matrix.

[0085] As a preferred implementation, the step of extracting key factors that affect travelers' decisions by calculating factor loading matrix based on the constructed factor model includes the following steps:

[0086] S231, calculating the covariance matrix of the data variables in the preprocessed multidimensional data set according to the preprocessed multidimensional data set;

[0087] S232, performing eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors;

[0088] S233. According to the size of the eigenvalue, select the eigenvectors corresponding to the first m largest eigenvalues ​​and form a factor loading matrix;

[0089] S234. Analyze the factor loading matrix and extract the key factors that affect travelers' decisions.

[0090] It should be noted that data preprocessing includes steps such as data cleaning (such as processing missing values ​​and outliers) and data conversion (such as standardization) to ensure data quality and accuracy of analysis.

[0091] Factor analysis is the use of exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) methods to extract key factors from multidimensional data. These factors represent potential dimensions that affect individual decision-making, such as personal preferences, psychological attitudes, etc. By determining the main factors that affect individual decision-making, the complexity of subsequent analysis is simplified, while retaining variables that have a significant impact on decision-making.

[0092] Among them, based on the multidimensional data set, the factor analysis method is used to extract the key factors that affect travelers' decision-making. The specific implementation steps are as follows:

[0093] First, standardize the variables in the data (such as gender, major, behavioral preferences, etc.) to ensure that the mean of each variable is 0 and the variance is 1.

[0094] Assume there are p observed variables X = (x1, x2, ..., x p ) T , these variables reflect the preferences and characteristics of individual travelers in multiple aspects of travel mode selection, and construct factor models to identify potential factors. These variables can be identified through m (m < p) common factors F = (f1, f2, ..., f m ) T , and a special factor (unique factor) vector u = (u1, u2, ..., u p ) T To express it, the factor model can be written as:

[0095] X = ΛF + u;

[0096] Among them, X represents the observed variable matrix (data variable matrix), Λ represents the loading matrix (reflecting the relationship between each factor and the observed variable), F represents the common factor, and u represents the error term. The loading matrix Λ and the factor common F are estimated by maximizing the common variance of the observed variables.

[0097] Principal Component Method: j=1,...,p is the sorted and standardized feature pair of the sample covariance matrix S. Let m<p be the number of common factors. Then the principal component solution of the factor loading matrix estimation is:

[0098] Where ^ represents the sample;

[0099] The estimate of the individual variance is The diagonal elements of in Commonality

[0100] Where S represents the sample covariance matrix;

[0101] represents the eigenvalues ​​of the sample covariance matrix;

[0102] represents the eigenvector of the sample covariance matrix;

[0103] represents the sample loading matrix;

[0104] Indicates that the variance of the original sample variable has not been portrayal part;

[0105] Indicates the individual shame of the sample, which is the part that cannot be contributed by the common factors;

[0106] S jj represents the total sample variance;

[0107] represents the sample commonality, the variance contributed by m common factors;

[0108] Represents the loading of the j-th variable of the sample on the k-th factor;

[0109] Represents the loading of the j-th variable of the sample on the m-th factor;

[0110] Represents the sample loading matrix The transpose of

[0111] represents the individual variance of the pth sample, where p is the number of original variables;

[0112] Represents the eigenvector of the mth sample covariance matrix;

[0113] Represents the eigenvalue of the m-th sample covariance matrix.

[0114] S3. Based on the extracted key factors, a factor equilibrium model is constructed using a mixed strategy, and the optimal travel strategy of travelers is obtained through model solving;

[0115] As a preferred implementation, the step of constructing a factor equilibrium model using a hybrid strategy based on the extracted key factors and solving the model to obtain the optimal travel strategy for travelers includes the following steps:

[0116] S31. Based on the extracted key factors, establish utility functions for different travel modes of travelers;

[0117] As a preferred implementation, the utility function is expressed as:

[0118] U iA =α i +β 1i F 1i +β 2i F 2i +ε iA ;

[0119] Where U iA represents the utility function of traveler i choosing travel mode A;

[0120] α i represents a constant term;

[0121] β 1i , β 2i The coefficients of the common factors F1 and F2 representing the choice of travel mode A;

[0122] ε iA represents a random interference term.

[0123] S32, establishing a mixed strategy, allowing travelers to choose between different travel modes with a pre-set probability, and calculating the expected utility of the travelers under the mixed strategy;

[0124] As a preferred implementation, the hybrid strategy is established to allow travelers to choose between different travel modes with a preset probability, and the formation of the hybrid strategy space includes the following steps:

[0125] S321, determine the travel mode of the traveler and construct a travel choice set;

[0126] S322. For each traveler, according to the constructed travel choice set, determine the probability of the traveler choosing different travel modes based on the probability distribution;

[0127] S323, the travel choices of all travelers are combined to form a mixed strategy space;

[0128] S324. Calculate the expected utility of the traveler under the mixed strategy through the expected utility function.

[0129] As a preferred implementation, the expression of the expected utility function is:

[0130] E[U iA ]=p i U iA +(1-p i ) iB ;

[0131] In the formula, E[U iA ] represents the expected utility of traveler i under the mixed strategy;

[0132] p i represents the probability that traveler i chooses travel mode A;

[0133] U iA represents the utility function of traveler i choosing travel mode A;

[0134] U iB represents the utility function of traveler i choosing travel mode B;

[0135] 1-p i represents the probability that traveler i chooses travel mode B.

[0136] S33. Based on the expected utility of travelers under mixed strategies, a factor equilibrium model is constructed and solved to obtain the Nash equilibrium result;

[0137] As a preferred implementation, the construction and solution of the factor equilibrium model based on the expected utility of the travelers under the mixed strategy to obtain the Nash equilibrium result includes the following steps:

[0138] S331, establishing constraint conditions according to the expected utility of the traveler under the mixed strategy, and calculating the traveler's choice probability according to the traveler's utility function;

[0139] S332, taking the choice probability of maximizing the utility function of the traveler as the objective function;

[0140] S333, establishing a factor equilibrium model according to the constraint conditions and the objective function;

[0141] S334. Solve the factor equilibrium model to obtain the Nash equilibrium result.

[0142] S34. Analyze the Nash equilibrium results and obtain the optimal travel strategy for travelers.

[0143] It should be noted that by defining the basic elements of the factor equilibrium model, including players (individuals or groups), strategies (possible behavioral choices) and payoff functions (the utility or satisfaction of each strategy),

[0144] The mixed strategy setting takes into account the uncertainty of individual behavior in real life and adopts the concept of mixed strategy Nash equilibrium, allowing individuals to choose between different strategies with a certain probability.

[0145] Specifically, solving the Nash equilibrium is to use mathematical and computational methods to solve the Nash equilibrium of the model (after factor analysis, the loading matrix is ​​obtained, and then the loading matrix is ​​used to map the standardized new data to the factor space and calculate the factor score.

[0146] The estimated parameters and (sample mean) is substituted into the weighted least squares method, Get a matrix of dimension n×m.

[0147] The influencing factors are then converted into the payment matrix of the Nash equilibrium in the mixed strategy through the set payment function, that is, the optimal strategy combination for each player given the strategies of other players.

[0148] By analyzing and predicting the optimal behavioral choices of individuals in specific situations (through the mixed strategy Nash equilibrium in game theory, the probability of each person's various behaviors in a certain population is obtained to maximize their benefits.), and how these choices are jointly influenced by personal factors and external conditions.

[0149] For example, suppose a game has N players, each of whom has a set of feasible strategies S i Under mixed strategies, player i chooses strategy s i ∈S i The probability is expressed as p i (s i );

[0150] Satisfy the conditions and p i (s i )≥0, for all strategies s i ∈S i .

[0151] The utility function of each player i is U i (p1, p2, .., p N ), where p i is the mixed strategy of player i. A Nash equilibrium is a strategy combination For all players, and any other strategy p i have:

[0152]

[0153] For travel mode selection:

[0154] Define utility function: Based on the factor analysis results, define the utility function for each travel mode. Assume that there are two main factors F1 and F2, and the two travel modes are A and B. The utility of traveler i choosing A or B can be expressed as:

[0155] U iA =α i +β 1i F 1i +β 2i F 2i +ε iA ;

[0156] U iB =γ i +δ 1i F 1i +δ 2i F 2i +ε iB ;

[0157] Where U iA represents the utility function of traveler i choosing travel mode A;

[0158] U iB represents the utility function of traveler i choosing travel mode B;

[0159] α i , γ i All represent constant terms;

[0160] β 1i , β 2i , δ1, δ2 represent the coefficients of the common factors F1 and F2 for choosing travel mode A or B;

[0161] ε iA , ε iB Both represent random interference terms.

[0162] The above parameters can be estimated by statistical analysis of survey data, such as least squares, maximum likelihood estimation, etc. Once the parameter estimation is completed, all the necessary parameters in the utility function are available. However, in mixed strategy Nash equilibrium, it is also necessary to determine the probability of each individual's allocation between different strategies, which usually involves solving an optimization problem, that is, maximizing the expected utility of each individual given the strategies of other individuals.

[0163] Mixed strategy definition: The probability that traveler i chooses A is p i , the probability of choosing B is 1-p i The expected utility under the mixed strategy is:

[0164] E[U iA ]=p i U iA +(1-p i ) iB ;

[0165] In the formula, E[U iA ] represents the expected utility of traveler i under the mixed strategy;

[0166] p i represents the probability that traveler i chooses travel mode A;

[0167] U iA represents the utility function of the traveler who chooses travel mode A;

[0168] U iB represents the utility function of traveler i choosing travel mode B;

[0169] 1-p i represents the probability that traveler i chooses travel mode B.

[0170] Solving Nash Equilibrium: Finding a Probability So that given the strategies of other travelers, no traveler can obtain higher expected utility by changing his strategy alone. For each traveler i, the mixed strategy selection is required to satisfy:

[0171]

[0172] Based on the above, it can be concluded that:

[0173]

[0174] The optimization problem is:

[0175]

[0176] Where N is the total number of samples of all surveyed travelers, U irepresents the utility function, and p represents the probability of choosing a transportation mode.

[0177] By solving the above optimization problem, we can find the probability of maximizing the utility function of all travelers and the corresponding Nash equilibrium (a person's choice of travel mode is affected by many factors, and there are 5 observable factors, but it actually reflects only one potential factor, such as personality. Therefore, we first reduce the dimension through factor analysis to simplify the analysis difficulty and increase the calculation efficiency. Then, the influencing factors after dimensionality reduction are set to be converted into the utility value brought by each person's choice of different travel modes, and then through multiple people's joint decision-making, the probability distribution of each person's choice of travel mode and the most probable travel mode are given to provide decision support for the deployment of corresponding transportation tools). In actual operation, the specific solution method depends on the form of the utility function and the structure of the game, which may include numerical optimization methods such as gradient descent method, Newton method, etc. Numerical solution and analysis can be carried out with the help of software computing tools such as MATLAB and Python mathematical library programming.

[0178] S4. Adjust the deployment strategy of transportation vehicles based on the optimal travel strategy of travelers.

[0179] Specifically, we conduct in-depth analysis based on the model results, such as exploring the probability of each person choosing a travel mode and deploying corresponding transportation tools based on each person’s maximum travel probability and population distribution.

[0180] Apply the model to actual decision support (deploy transportation vehicles based on the distribution of travel mode selection probabilities), such as marketing strategy formulation, public policy planning, personalized service design, etc.

[0181] By verifying the effectiveness of the model and applying the insights of the model to practical problem solving and decision optimization, a scientific basis is provided for decision makers.

[0182] In order to facilitate understanding of the above technical solution of the present invention, the implementation method of the present invention in the actual process is described in detail below:

[0183] Based on actual conditions, the survey collected 835 questionnaires and collected samples of different genders, majors, and preferences about the selection strategies of the two modes of transportation under different pricing strategies. A data set was established and Python programming was used to preliminarily test the feasibility and predictive analysis capabilities of the factor equilibrium model.

[0184] The questionnaire design is shown in Table 1-Table 6:

[0185] Table 1 Travel behavior impact questionnaire

[0186]

[0187] Table 2 Risk preference questionnaire

[0188]

[0189]

[0190] Table 3 Questionnaire on intention to choose transportation

[0191]

[0192]

[0193] Table 4 Questionnaire on intention to choose transportation

[0194]

[0195] Table 5 Questionnaire on intention to choose transportation

[0196]

[0197] Table 6 Questionnaire on intention to choose transportation

[0198]

[0199] Standardize the coding of data;

[0200] Gender: male=1, female=0;

[0201] Major: Natural science = 1, Humanities = 0;

[0202] BR1: I am brave enough to try new things;

[0203] BR2: I often tend to choose challenging things;

[0204] BR3: I always respond to uncertainty with bold and decisive actions;

[0205] BR4: I always challenge myself regardless of age;

[0206] BR5: I always have confidence in myself;

[0207] The values ​​in columns BR1, BR2, BR3, BR4, and BR5 are all five-point Likert scales, specifically: strongly disagree = 0;

[0208] Somewhat disagree = 1;

[0209] Uncertain = 2;

[0210] Basically agree = 3;

[0211] Strongly agree = 4;

[0212] AvL4: Will choose L4 level supervised autonomous driving = 1, will not choose = 0;

[0213] AvL5: Will choose L5 level supervised autonomous driving = 1, will not choose = 0;

[0214] taxi_27_L4_35: The travel cost for the same distance is 27 yuan for a taxi and 35 yuan for L4 autonomous driving. Select L4 autonomous driving = 1, select taxi = 0;

[0215] taxi_20_L5_27: The travel cost for the same distance is RMB 20 for a taxi and RMB 27 for L5 autonomous driving. Select L5 autonomous driving = 1, select taxi = 0;

[0216] L4_16_L5_39: The travel cost for the same distance is 16 yuan for L4 level autonomous driving and 39 yuan for L5 level autonomous driving. Select L4 level autonomous driving = 1, select L5 level autonomous driving = 0;

[0217] First, the data is cleaned and a preliminary statistical analysis is performed, as shown in Table 7:

[0218] Table 7 Statistical analysis table

[0219]

[0220] Modeling and analysis according to the steps of factor analysis model: Python code is used this time, and some code examples are as follows:

[0221]

[0222]

[0223]

[0224]

[0225] Model analysis results:

[0226] Player 1: The probability of choosing an autonomous vehicle is higher;

[0227] Player 2: More likely to choose an autonomous vehicle;

[0228] Interpretation of results and further analysis:

[0229] Two people randomly selected from the test participants are more likely to choose self-driving cars. This observation may indicate that self-driving cars are highly accepted and preferred as an emerging mode of transportation in the test group. This tendency may stem from curiosity about new technologies, trust in the safety of self-driving cars, or recognition of the convenience and safety they provide.

[0230] In addition, other key influencing factors should be considered. First, the probability of selecting an autonomous vehicle can reflect the user's acceptance of the technology. Second, this may also be related to the demographic characteristics of the tested population, such as age, educational background, and technology familiarity. In addition, environmental factors such as traffic conditions at the test site, available transportation options, and geographic location may also affect people's choices.

[0231] Therefore, in-depth analysis of this data will not only help understand the current market acceptance of autonomous vehicles, but also provide a basis for future marketing strategies. For example, if younger and more educated groups are more likely to use autonomous vehicles, marketing and product customization targeting this group may be more effective.

[0232] Practical significance;

[0233] This analysis based on actual survey questionnaires and factor equilibrium models provides a method to understand and predict the travel mode choices of travelers under different preferences. This analysis can help travel service providers and urban planners better understand the needs and preferences of travelers, so as to provide more personalized and user-friendly services.

[0234] In addition, the advantages and disadvantages of the model in this invention are summarized as follows:

[0235] Model efficiency;

[0236] 1. Computational efficiency: Factor analysis, as a dimensionality reduction technique, can effectively reduce the number of variables that need to be processed for analysis and improve the efficiency of model operation. The computational complexity of the mixed decision Nash equilibrium model mainly depends on the number and complexity of strategies. For simplified scenarios (such as the two strategies in this survey), the computational efficiency is relatively high.

[0237] 2. Data utilization: The model improves data utilization efficiency by utilizing existing data features, extracting key factors and applying them to travel decision analysis.

[0238] 3. Adaptability: The model has a certain degree of adaptability and can adjust the specific settings of factor analysis and mixed decision Nash equilibrium model according to different data sets and analysis requirements.

[0239] Model advantages:

[0240] 1. Theoretical innovation: Combining factor analysis and game theory to study travel mode selection provides a new analytical perspective and method.

[0241] 2. Decision Depth: By identifying the key factors that influence travel choices and analyzing how these factors interact among different travelers, the model can explain the decision-making behavior of travelers.

[0242] 3. Flexibility: The model can be adjusted according to different research needs and data conditions, and has good flexibility and adaptability.

[0243] Model Disadvantages:

[0244] 1. Complexity and difficulty in understanding: The increased complexity of the model places higher demands on the understanding and interpretation of the model.

[0245] 2. Data requirements: Although factor analysis can improve data utilization, the effectiveness and accuracy of the model still rely on high-quality and highly relevant data, which puts more stringent requirements on the design of the questionnaire and the implementation of the plan.

[0246] 3. Simplification of strategy setting: In order to reduce the difficulty of model construction and management, mode selection and travel cost-utility function may be simplified.

[0247] In summary, with the help of the above technical solution of the present invention, the present invention uses the factor equilibrium model to explore the influence of various factors on individuals when choosing travel modes, so as to find the travel behavior strategy with the highest probability of participants, so as to provide a reference for the investment of corresponding transportation tools. The purpose of this model is to understand and explain the travel behavior of individuals under different selection conditions, and provide the probability distribution of the number of people who choose different travel modes, so as to provide a reference for formulating traffic policies or promoting new transportation modes. By analyzing the factor equilibrium model, we can deeply understand the individual's preference for different travel modes, as well as the influence of factors such as gender, profession, and personal psychology on travel choices, so as to provide important decision support for optimizing urban traffic management and improving traffic efficiency. The present invention adopts mixed strategy modeling technology, the mixed strategy modeling technology involved in the factor equilibrium model, obtains the load parameters for selecting different transportation modes from the factor analysis results, and participates in the mixed strategy Nash equilibrium model to solve. At the same time, this is also a method of data dimensionality reduction analysis, which can analyze and select common latent variable data from a variety of data for dimensionality reduction, and then analyze the overall optimal response measures through probability distribution.

[0248] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, optical storage, etc.) containing computer-usable program code.

[0249] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining traveler choice tendency using a factor equilibrium model, characterized in that: The method of using the factor equilibrium model to discriminate travelers' choice tendency includes the following steps: S1. Collect the travel choice data of travelers and obtain a multidimensional data set through data collation; S2, based on multidimensional data sets, using factor analysis to extract key factors that affect travelers’ decisions; S3. Based on the extracted key factors, a factor equilibrium model is constructed using a mixed strategy, and the optimal travel strategy of travelers is obtained through model solving; S4. Adjust the deployment strategy of transportation vehicles based on the optimal travel strategy of travelers.

2. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 1, characterized in that: The method of extracting key factors affecting travelers' decision-making based on a multidimensional data set using factor analysis includes the following steps: S21, preprocessing the data variables in the multidimensional data set; S22, constructing a factor model based on the preprocessed multidimensional data set; S23. Based on the constructed factor model, the key factors that affect travelers’ decision-making are extracted by calculating the factor loading matrix.

3. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 2, characterized in that: The preprocessing of the data variables in the multidimensional data set comprises the following steps: S211, performing data cleaning processing on the data variables in the multidimensional data set, including processing of missing values ​​and outliers; S212, performing standardization processing on the data variables in the multidimensional data set after data cleaning to obtain standardized data; The mean value of each data variable in the standardized data is 0 and the variance is 1.

4. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 2, characterized in that: The expression of the factor model is: X = ΛF + u ； In the formula, X represents the data variable matrix; Λ represents the load matrix; F represents the common factor; u Represents a special factor.

5. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 2, characterized in that: The method of extracting key factors that affect travelers' decisions by calculating the factor loading matrix based on the constructed factor model includes the following steps: S231, calculating the covariance matrix of the data variables in the preprocessed multidimensional data set according to the preprocessed multidimensional data set; S232, performing eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors; S233, according to the size of the eigenvalue, select the front m The eigenvectors corresponding to the largest eigenvalues ​​form the factor loading matrix; S234. Analyze the factor loading matrix and extract the key factors that affect travelers' decisions.

6. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 1, characterized in that: The method of constructing a factor equilibrium model using a hybrid strategy based on the extracted key factors and solving the model to obtain the optimal travel strategy for travelers includes the following steps: S31. Based on the extracted key factors, establish utility functions for different travel modes of travelers; S32, establishing a mixed strategy, allowing travelers to choose between different travel modes with a pre-set probability, and calculating the expected utility of the travelers under the mixed strategy; S33. Based on the expected utility of travelers under mixed strategies, a factor equilibrium model is constructed and solved to obtain the Nash equilibrium result; S34. Analyze the Nash equilibrium results and obtain the optimal travel strategy for travelers.

7. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 6, characterized in that: The expression of the utility function is: U iA = α i + β 1i F 1i + β 2i F 2i + ε iA ； In the formula, U iA Indicates travelers i The utility function for choosing travel mode A; α i represents a constant term; β 1i , β 2i Indicates the choice of travel mode A The common factor F 1 and F The coefficient of 2; ε iA represents a random interference term.

8. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 6, characterized in that: The hybrid strategy is established to allow travelers to choose between different travel modes with a pre-set probability. The hybrid strategy space is formed by the following steps: S321, determine the travel mode of the traveler and construct a travel choice set; S322. For each traveler, according to the constructed travel choice set, determine the probability of the traveler choosing different travel modes based on the probability distribution; S323, the travel choices of all travelers are combined to form a mixed strategy space; S324. Calculate the expected utility of the traveler under the mixed strategy through the expected utility function.

9. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 8, characterized in that: The expression of the expected utility function is: E [ U iA ]= p i U iA +(1- p i ) U iB ； In the formula, E [ U iA ] indicates travelers i Expected utility under mixed strategies; p i Indicates travelers i Choose your travel method A probability; U iA Indicates travelers i Choose your travel method A The utility function of U iB Indicates travelers i Choose your travel method B The utility function of 1- p i Indicates travelers i Choose your travel method B probability.

10. The method for determining traveler's choice tendency using a factor equilibrium model according to claim 6, characterized in that: The construction and solution of the factor equilibrium model based on the expected utility of the travelers under the mixed strategy to obtain the Nash equilibrium result includes the following steps: S331, establishing constraint conditions according to the expected utility of the traveler under the mixed strategy, and calculating the traveler's choice probability according to the traveler's utility function; S332, taking the choice probability of maximizing the utility function of the traveler as the objective function; S333, establishing a factor equilibrium model according to the constraint conditions and the objective function; S334. Solve the factor equilibrium model to obtain the Nash equilibrium result.

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