Classifying one variable into two different parts with physical meaning

by Han Zhengzu   Last Updated May 16, 2018 14:19 PM

I'm not very proficient in statistic analysis. To deal with a practical problem, I presented the background here for some advice.

Background

I'm working on the measurements of atmospheric pollutant and the identification of their sources. For a specific atmospheric species $A$, its origins are very complex and can be divided into two categories:

(1) directly emitted from the human activities, e.g., vehicle pipeline, industrial processes.

(2) $A$ is not emitted from the ground, but as the result of transformation of other species in the atmosphere.

Therefore, A as the combination of primary-emitted A ($A_p$) and secondary-formed A ($A_S$). To estimate the fractions of $A_p$ and $A_s$ are crucial for air quality management, while there is no direct method to distinguish them by current instructments.

My thought

Since dividing A into two parts is hard using chemical analysis, I tried to think about the statistic approach to solve the problem.
$$A = A_{p}+A_{s}$$

I also measured other species, e.g., $P_1, P_2$ which is mainly originated from direct emission, and stable in the atmosphere, and connected with $A_s$; $S_1, S_2$ which is mainly from the secondary formation, and connected with $A_s$.

For the time series of $A, P_1, P_2, S_1, S_2$, I thought to predict $A_p$ by $B$, and $A_s$ by $C$ would be a meaningful approach to divide $A$. In some previous work, I knew that MLR could be an option as:
$$A_{p,\ predict} = (a+b*P_1+c*P_2)$$ $$A_{s,\ predict} = (d+e*S_1+f*S_2)$$ while the sum of $A_{p,\ predict}$ and $A_{s,\ predict}$ was not expected to be the measured $A$ in the time series.

Are there any suitable and advanced methods to tackle my problem?



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