| Literature DB >> 34911564 |
Abstract
BACKGROUND: Standardization and normalization of continuous covariates are used to ease the interpretation of regression coefficients. Although these scaling techniques serve different purposes, they are sometimes used interchangeably or confused for one another. Therefore, the objective of this study is to demonstrate how these scaling techniques lead to different interpretations of the regression coefficient in multilevel logistic regression analyses.Entities:
Keywords: Multilevel analysis; Neighborhood socioeconomic status; Normalization; Standardization
Year: 2021 PMID: 34911564 PMCID: PMC8672510 DOI: 10.1186/s13690-021-00750-w
Source DB: PubMed Journal: Arch Public Health ISSN: 0778-7367
Description of a hypothetical data (3000 individuals)
| Health Condition | |
| Favorable | 70.0% |
| Unfavorable | 30.0% |
| Trait 1 | |
| Minimum | 25.0 |
| Mean | 42.1 |
| Median | 41.0 |
| Maximum | 65.0 |
| Trait 2 | |
| Group 1 | 50.0% |
| Group 2 | 50.0% |
| Trait 3 | |
| Group 1 | 30.5% |
| Group 2 | 28.2% |
| Group 3 | 30.8% |
| Group 4 | 10.5% |
| Trait 4 | |
| Group 1 | 13.5% |
| Group 2 | 20.2% |
| Group 3 | 23.6% |
| Group 4 | 29.4% |
| Group 5 | 13.4% |
Fig. 1Correlation plot and histogram of two measures of neighborhood socioeconomic status in St. Louis, MO (382 census tracts). SEP = a composite measure of socioeconomic position [34]. MHI− 1 = median household income divided by − 1 [35]
Simulation analyses of the association between neighborhood socioeconomic status and health condition in St. Louis, MO (3000 individuals across 300 census tracts)*
| Model 1 | Model 2 | Model 3 | Model 4 | ||
|---|---|---|---|---|---|
| OR (95% CI) | OR (95% CI) | OR (95% CI) | OR (95% CI) | ||
| SEP | (standardized) | 1.32 (1.17, 1.48) | |||
| MHI−1 | (standardized) | 1.35 (1.14, 1.60) | |||
| SEP | (normalized) | 3.26 (1.93, 5.50) | |||
| MHI−1 | (normalized) | 3.70 (1.78, 7.70) | |||
| Trait 1 | 1.03 (1.02, 1.04) | 1.03 (1.02, 1.04) | 1.03 (1.02, 1.04) | 1.03 (1.02, 1.04) | |
| Trait 2 | Group 1 | Ref. | Ref. | Ref. | Ref. |
| Group 2 | 1.22 (1.02, 1.45) | 1.22 (1.03, 1.46) | 1.22 (1.02, 1.45) | 1.22 (1.03, 1.46) | |
| Trait 3 | Group 1 | Ref. | Ref. | Ref. | Ref. |
| Group 2 | 1.20 (0.94, 1.52) | 1.21 (0.95, 1.54) | 1.20 (0.94, 1.52) | 1.21 (0.95, 1.54) | |
| Group 3 | 1.24 (0.97, 1.57) | 1.27 (1.00, 1.61) | 1.24 (0.97, 1.57) | 1.27 (1.00, 1.61) | |
| Group 4 | 1.43 (1.03, 1.98) | 1.49 (1.07, 2.05) | 1.43 (1.03, 1.98) | 1.49 (1.07, 2.05) | |
| Trait 4 | Group 1 | Ref. | Ref. | Ref. | Ref. |
| Group 2 | 1.10 (0.80, 1.52) | 1.10 (0.80, 1.52) | 1.10 (0.80, 1.52) | 1.10 (0.80, 1.52) | |
| Group 3 | 1.24 (0.91, 1.71) | 1.25 (0.91, 1.72) | 1.24 (0.91, 1.71) | 1.25 (0.91, 1.72) | |
| Group 4 | 1.19 (0.86, 1.64) | 1.24 (0.90, 1.70) | 1.19 (0.86, 1.64) | 1.24 (0.90, 1.70) | |
| Group 5 | 1.38 (0.95, 2.02) | 1.47 (1.01, 2.14) | 1.38 (0.95, 2.02) | 1.47 (1.01, 2.14) | |
| Variance (SE) | Variance (SE) | Variance (SE) | Variance (SE) | ||
| Census Tract | 0.257 (0.507) | 0.276 (0.525) | 0.257 (0.507) | 0.276 (0.525) | |
| Akaike information criterion | 3527.677 | 3534.992 | 3527.677 | 3534.992 | |
| Bayesian information criterion | 3599.753 | 3607.069 | 3599.753 | 3607.069 | |
| Log-Likelihood | − 1751.838 | − 1755.496 | −1751.838 | −1755.496 | |
| Deviance | 3503.677 | 3510.992 | 3503.677 | 3510.992 | |
*When analyzing the actual health data, multilevel models must adjust for (account for) individual-level socio-demographic characteristics (e.g., age, gender, race/ethnicity, educational attainment, income level, marital status, and/or occupational category)
Ref. reference group
SE standard error
OR odds ratio
CI confidence interval
SEP a composite measure of socioeconomic position [34]
MHI median household income divided by − 1 [35]