This article is a short review of the paper “Spatio-temporal analysis of rail station ridership determinants in the built environment, Yadi Zhu et al”
It is quite hard to figure out a model when it comes to a transportation domain. An estimate of the arrival time, Ridership prediction — alignment, delivery route optimization, and so on. This is all because of the spatial(spatio)-temporal properties embedded in the model.
The first thing you can think of is the statistical model with variants. Here, that variants are temporal factors and spatial factors.
Base Model
The basic model is a simple linear regression model with particular variants designed for spatio properties: Land-use entropy
where E is the land-use entropy of each station, p_j is the proportion of land-use category j such as residential land, industrial land, land for road, etc.
It turns out that the linear model violates the normal error assumption so we have to now consider another model: negative binomial model
Bayesian negative binomial regression (B-NBR)
This is negative binomial model within Bayesian framework to discover the factors that impact the station ridership at different times of the day.
bayesian: exponential of epsilon(exp_ε) follows a gamma distribution with a mean of 1 and variance and ⍺(alpha is an over-dispersion parameter and the inverse ⍺ follows a prior gamma distribution of (0.5, 0.0005) )
Based on these models, significant factors impacting station ridership at different times of the day are chosen for spatial impact analysis.
Geographic weighted negative binomial regression (GW-NBR)
Also, geographically weighted Poisson regression is developed. Here, coefficient parameter values that vary with the geographical location were introduced to develop a GW-NBR model for spatial impact analysis on station ridership.
where u(u_x,u_y) is a vector of two-dimensional coordinates describing the location of stations s. So, coefficients vary with the location. A weighted least-squares method is used to estimate the coefficients.
Following theoretical modeling, the authors discuss the results. It is a good model and they were able to extract insights from the model. I got the point.
Let me know if you have more interest on this kind of analysis.
