Dear Sir/Mam,
In secondary data time series analysis, when should we use static regression model and when should we use other regression models ( distributed lag or auto regressive distributed lag model)
Regarding application of distributed lag model, following studies maybe useful
1. A spatially varying distributed lag model with application to an air pollution and term low birth weight study.
PMID: 32595237 Free PMC article.Warren JL, Luben TJ, Chang HH.J R Stat Soc Ser C Appl Stat. 2020 Jun;69(3):681-696. doi: 10.1111/rssc.12407. Epub 2020 Mar 30.
2. Distributed Lag Linear and Non-Linear Models in R: The Package dlnm.
PMID: 22003319 Free PMC article.Gasparrini A.J Stat Softw. 2011 Jul;43(8):1-20.
3. Distributed lag non-linear models.
PMID: 20812303 Free PMC article.Gasparrini A, Armstrong B, Kenward MG.Stat Med. 2010 Sep 20;29(21):2224-34. doi: 10.1002/sim.3940.
4. Applying the Distributed Lag Non-Linear Model (DLNM) in Epidemiology: Temperature and Mortality in Mashhad.
PMID: 31970119 Free PMC article. No abstract available.Entezari A, Mayvaneh F.Iran J Public Health. 2019 Nov;48(11):2108-2111.
5. Modelling malaria incidence by an autoregressive distributed lag model with spatial component.
PMID: 28760265Laguna F, Grillet ME, León JR, Ludeña C.Spat Spatiotemporal Epidemiol. 2017 Aug;22:27-37. doi: 10.1016/j.sste.2017.05.001. Epub 2017 Jun 8.
When the response variables are autocorrelated (e.g., data collected over varying times or space), and also cross correlated with the predictors at their lagged values, typically distributed lag models will be more useful than static models. Basically, if you data set is like (y_t, x_t), t=1,2,... where y_t is the response at time t and x_t is the predictor (vector) at time t, then if you find y_t depends on y_{t-l} and/or x_{t-l} for lag values l=0,1,2,.., then use the distributed lag model. If you are familiar with R check out this package:
Article dLagM: An R package for distributed lag models and ARDL bounds testing
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