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Federal Register / Vol. 86, No. 142 / Wednesday, July 28, 2021 / Rules and Regulations
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9. The Commissions outlier procedure identifies and removes a total of 25
observations 22 jails with average daily populations less than 1,000, and 3 larger jails. This amounts to 1.6% of observations of larger jails and 0.8% of observations of jails with average daily populations less than 1,000. The outlier procedure removes three contracts for larger jails operated by Correct.
The remaining 22 observations are all jails with average daily populations less than 1,000 whose per-minute costs also fall outside of the bounds of all three outlier detection methods.
10. It is evident that the outlier contracts have average per-minute costs that are significantly above the norm. All of the larger jails have revenues per minute below their per-minute costs, suggesting the cost data are unreliable in these cases. Of the jails with average daily populations less than 1,000, 11
have per-minute revenues that are less, and in some cases substantially less, than their per-minute costs, again suggesting that their costs are unlikely to be valid. The remaining outliers also have per-minute costs that are well outside of the central tendency of the data, adding further validity to the Grubbs procedure.
1. GTL Data Adjustment 11. Though the Commission believes the contract-level cost data to be improved after removing the outlier observations, the Commission finds the costs reported by certain contracts that are not identified as outliers to be outside of what is reasonable given comparable contracts in the data.
Specifically, GTLs per-minute costs for its prison contracts, as calculated using the data GTL reported, are significantly higher than per-minute costs calculated based on data submitted by providers operating similarly sized facilities. Likewise, both GTL and REDACTED are high-cost providers for larger jails. REDACTEDs average costs per minute for larger jails drop to a lower level after the removal of the three larger jail contracts in the outlier analysis. However, REDACTED only has two such contracts while GTL has 62. As such, while REDACTEDs inconsistent larger jail contracts should be explored, they do not have nearly as significant an effect on overall costs per minute as do GTLs contracts. GTL, REDACTED, and REDACTED are also the highest-cost providers of inmate calling services for smaller jails, but those contracts are not the primary focus of this analysis.
12. To illustrate the large discrepancy between GTLs per-minute costs for prison and larger jail contracts and those of all other providers, the Commission presents the histograms in Figure 1 below. Rather than a normal distribution of per-minute costs across contracts, the histograms appear bimodal due to GTLs costs. GTLs average per-minute costs for prisons and larger jails are about REDACTED as large as those of all other providers. In fact, for prisons, GTLs least costly contract is still higher than any other providers most costly contract.
Figure 1Cost per Minute CPM
Distributions for Prisons and Larger Jails REDACTED

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Notes: CPM is the cost per minute. Dark red areas are where the Non-GTL and GTL
bars overlap.
13. Given the large discrepancy between GTLs costs and those of all other providers, the Commission finds it implausible that GTLs actual cost of providing inmate calling services to prisons and larger jails is as high as its reported data suggest. Therefore, in order to address GTLs costs, the Commission implements a k-nearest neighbor matching algorithm to match each GTL contract to multiple other contracts by non-GTL
providers based on similar contract characteristics. More formally, the multivariate k-nearest neighbor regression is a non-parametric method that uses the Euclidian distance between continuous variables to determine the closeness of observations. It is a well-established approach to data imputation issues, where missing or unreliable observations need to be replaced with plausible values from the same dataset. The Commission implements the knearest neighbor approach to find contracts similar to GTLs and then adjust GTLs perminute costs based on the per-minute costs of those other contracts. In their attempt to address outliers, the report of The Brattle Group utilizes a data censoring technique known as winsorization to replace all perminute cost observations above $0.50 with the next highest values in the cost distribution. The Commission believes a combination of outlier removal and cost adjustment using k-nearest neighbor regression to be an improvement over winsorization. Whereas winsorization replaces a set percentage or number of observations above a predetermined threshold, the Grubbs procedure relies on the variation in the data to determine observations likely drawn from a different population distribution. Likewise, k-nearest neighbor relies on a multivariate measure of the closeness of contracts to determine the adjustment to GTL observations, making fewer assumptions and utilizing more information in the contracts.
14. The Commission performs the analysis with k = 3. That is, the Commission finds the three nearest neighbors to each GTL contract.
The matching is done on the following variables: Average daily population, total inmate calling services minutes of use, total commissions paid, and facility type. The Commission has also performed the analysis with the addition of other variables such as revenues, geography, and rurality, and obtained similar results. In the case of encoded categorical variables such as geography, the Commission forced the algorithm to make a match to ensure that the distance measure was not attempting to minimize distance between unrelated states/
regions based on how they were coded in the dataset. Though the resulting adjusted perminute costs were largely unchanged, this is not the preferred specification as forcing a match on any given dimension will invariably weaken the match on the other covariates. Additionally, while the Lasso analysis set forth in Appendix B pointed to provider identity as the dominant predictor of a contracts per minute costs, the Commission does not match on provider
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identity. The Commission finds no economic rationale for why certain providers should have higher costs than their competitors for comparable facilities, nor do comments filed with the Commission make this argument.
Furthermore, as explained in Appendix B, the importance attributed to provider identity by the Lasso model is most likely the result of asymmetric provider data filing practices, rather than actual differences in costs of provision. A neighbor to a specific GTL
contract is the contract that is closest to the GTL contract along these dimensions. For example, if a GTL contract had an average daily population of 100, 15,000 total minutes, and paid $3,000 in site commissions, then another contract with an average daily population of 110, 16,000 total minutes, and paid site commissions of $3,400 would be a nearer neighbor than a third contract with an average daily population of 600, 100,000
minutes, and paid site commissions of $18,000. Matching was done on these four variables, as economic rationale and comments submitted to the Commission argue that each of the four is important in determining a contracts cost of provision.
Numerous commentators argued that average daily population and facility type are important to a contracts per minute costs.
Total minutes of use is included because inmate calling contracts have high fixed costs. As such, a contracts per minute costs will depend in part on minutes of use, as higher minutes of use allow fixed costs to be spread across more minutes, reducing a contracts per minute costs. Total commissions paid is included because, as first concluded in the 2020 ICS FNPRM, site commissions may represent negotiations between providers and facility authorities in which providers agree to incur additional costs related to the provision of inmate calling services in exchange for not having to pay site commissions. The Commission creates two adjusted per-minute costs for GTL. The first takes a weighted average cost per minute of each nearest neighbor, weighted by each neighbors inverse distance from GTL. That is, of the three nearest neighbors, the Commission put more weight on the neighbors that are more similar to GTL
according to the Euclidian distance measure.
The second approach is more conservative and relies on the maximum cost per minute of all nearest neighbors. The Commission has run the matching on various values of k and find the results are robust to the choice of k.
Even at k = 6, the Commission obtains reasonable results for the maximum perminute cost of the six nearest neighbors.
Though as expected, when adding more neighbors, the maximum per-minute cost of the new group of neighbors continues to increase. As this is not a classification analysis, there is no methodology or metric for choosing the optimal k. However, the Commission finds k = 3 to be reasonable. The Commissions choice is further supported by the use of k = 3 in the existing literature.
Table 4 presents summary statistics for GTLs original per-minute costs for non-outlier prison and larger jail contracts, as well as the weighted and maximum costs per minute that result from the nearest neighbor matching algorithm.

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