May I know the significance of "Block Size" while running the base model bootstrap. I have noticed that the change in block size changes the results.
Please may I know what is its significance and what will be the appropriate way to run the bootstrap run?
Dear friend Pradeep Attri
In bootstrapping, the block size refers to the number of observations that are resampled together as a group. This parameter can have an impact on the results obtained from a bootstrap analysis.
A small block size can lead to increased variance in the bootstrap estimates, while a large block size can lead to a loss of information and decreased accuracy in the estimates. Generally, a block size of around 10-30% of the total sample size is recommended for most applications.
The appropriate block size can depend on the specific data and research question being investigated. It may be helpful to try different block sizes and compare the results to determine the optimal size for a given analysis.
Here are some references that discuss the significance of block size in bootstrap analysis:
Hi Kaushik Shandilya
May I know if will "block size" depend on the number of samples and if so may I know what is the minimum number of samples that are appropriate to run the PMF model?
As noticed change in the block size affects the unmapped values. I have observed the unmapped values are more in case of default block size value ( which is 2). but as I increase the Block size, unmapped runs start to reduce.
Thank you so much for your response on Block size. it's really helpful.
Dear friend Pradeep Attri
The block size in the PMF model does not necessarily depend on the number of samples, but it can be influenced by the complexity of the data and the variability in the sources of the data. A larger block size may be useful in capturing more complex relationships in the data, but it may also result in slower computation times and more difficulties in mapping the data. The appropriate block size can depend on the specific data and research question, and there is no single answer for the minimum number of samples that is appropriate to run the PMF model. It is generally recommended to have a minimum of 50-100 samples, but this can vary depending on the complexity and variability of the data.
Regarding the unmapped values, increasing the block size may help to reduce the number of unmapped runs, but it may also result in a loss of information or resolution in the data. The appropriate block size should be chosen based on a trade-off between reducing unmapped runs and maintaining sufficient resolution in the data.
I would suggest consulting the literature on PMF modeling for further guidance on selecting an appropriate block size and minimum number of samples. Some relevant references include:
- Paatero, P., & Tapper, U. (1994). Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 5(2), 111-126.
- Hopke, P. K. (2016). Recent developments in receptor modeling. Journal of the Air & Waste Management Association, 66(2), 105-123 (He was my professor, one of the best professors I was taught from).
- Brown, S. G., Eberly, S. I., & Paatero, P. (2015). The identification of sources of air pollution by positive matrix factorization of hourly monitor data. Environmental science & technology, 49(6), 3830-3838.
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