Air Quality Data Analysis Based On The Mixed Factor Model

Heterogeneous data exist in many fields,such as psychology and environmental science.Mixture factor models that combine latent classes in factor analyses can be used to explore population heterogeneity.In this paper,the covariates are introduced based on the mixture factor model.This mixture factor model with covariates can simultaneously consider the underlying factors causing data heterogeneity and the observable influencing factors in the process of exploring heterogeneous data.It effectively avoids the loss of data information.A two-step estimation procedure is developed for the model and its validity is illustrated by various simulation studies.We also apply these mixture factor models to the quality assessment of city air.First,from the perspective of the mixture factor model,we objectively solve the classification problem of city air quality according to the summarized information.Because of the characteristic of the model,so that it avoids the unfairness of cities that have AQIs near some pre-determined threshold.Then,we study the relationship between the air quality and meteorological factors via the mixture factor model with covariates.The results show that pressure,temperature,relative humidity and precipitation have significant influence on air quality with corresponding influence arranged in a descending order.At the same time,we discuss that the model is more suitable than multivariate multiple linear regression model for this kind of problems,and the model has good applicability.