## 6 Conclusions  
The proposed RASMR approach manages to generate more accurate estimates of parameters due to better-quality representatives after additional model-specific splitting. The estimation accuracy improves along with the increasing number of iterations. For data with a relatively simple structure, typically a small number of iterations can provide accurate enough estimates for further data analysis, including model selection. For data with a more complicated structure or a larger number of parameters, we recommend an increased number of iterations and an exponential learning rate decay to ensure better convergence behavior. For a practical implementation of RASMR, \(K\)-means clustering may consume a considerable amount of time. When a natural partition is not available, we recommend small \(K\)-means clustering or correlation-based quantile split for a faster clustering process (see Section S1 in the Supplementary Materials for more details). When the number of covariates or predictors is large, we recommend the correlation-based quantile split strategy due to its fast speed. When applying RASMR to the model selection, we recommend RASMR with the delta ratio split. A default threshold of delta ratio is 1 since the delta ratios rarely go beyond 1 for typical applications. When the competing models have very close performance, we recommend a smaller threshold, such as 0.1, to ensure better-quality representatives. A key step with RASMR is to construct a good set of representatives and find an accurate approximation \(\widehat{\boldsymbol{\beta}}\) for the MLE \(\widehat{\boldsymbol{\beta}}\) based on the full data. When some collinearity exists among the covariates or predictors, \(\widehat{\boldsymbol{\beta}}\) may not be unique and the RASMR algorithm may encounter an identifiability issue. It is worth exploring how to adjust RASMR for variable selection under the presence of collinearity. The proposed RASMR approach is especially useful for analyzing big data with binary responses, such as intrusion detection for cyber security [59] and fraud detection for insurance companies [60]. Nevertheless, when the responses have three or more categories, the data may be modeled by multinomial logistic models [61; 62; 63] instead of GLMs. In this case, it is challenging to construct representatives for given data blocks that are more efficient than the corresponding mean representatives. **Supplementary Materials:** The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/a17100456/s1](https://www.mdpi.com/article/10.3390/a17100456/s1)]([https://www.mdpi.com/article/10.3390/a17100456/s1](https://www.mdpi.com/article/10.3390/a17100456/s1)), including more discussions on S1. Generating Data Blocks; S2. More on Delta Ratio Split; S3. More on Link Function Selection; S4. More on Variable Selection Using RASMR; S5. More Simulation Studies; S6. Proofs and Relevant Lemmas; S7. More on Airline Data; S8. More Figures [64; 65; 66; 67; 68; 69; 70; 71; 72; 73]. Figure 3: Trend of log(RMSE) for SMR and RASMR estimations under different link functions for the first 60 months with quantile split clustering. **Author Contributions:** Conceptualization, D.Z., K.L. and J.Y. ; methodology, D.Z. and J.Y. ; software, D.Z. and K.L. ; validation, D.Z. ; formal analysis, D.Z. ; investigation, D.Z. and J.Y. ; resources, K.L. and J.Y. ; data curation, D.Z. ; writing--original draft preparation, D.Z. and J.Y. ; writing--review and editing, K.L. and J.Y. ; visualization, D.Z. ; supervision, J.Y. ; project administration, J.Y. ; funding acquisition, J.Y. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded in part by the U.S. NSF grant DMS-1924859.