Linear Regression Of Log-transformed Data Research Articles

Methods you can count on: A simulation experiment showing the advantages generalized linear modeling (GLM) over the linear regression of log-transformed count data

Count data are the oldest and most basic form of data in the field of archaeology. Count data, however, have long been known to defy the assumptions of many commonly used parametric statistical methods, such as linear regression, in generally failing to follow a normal distribution. Most archaeological analyses have dealt with this problem through the logarithmic transformation of count data for the purposes of normalization. Recently, other scientific fields have recognized major shortcomings associated with log transformation and they have adopted nonparametric alternatives, such as generalized linear modeling (GLM). With a few exceptions, the field of archaeology has not followed suit. This paper presents the results of a simulation experiment designed to compare the performance of linear regression of log-transformed data and GLM under some commonly occurring conditions for count data in the field of archaeology. The results of this simulation experiment confirm the striking superiority of GLM compared with the linear regression of log-transformed data, showing that the latter is particularly prone to false-negative results (i.e. Type II error). We argue that archaeologists, therefore, should join other scientific fields in more widely adopting GLM and its nonparametric counterparts in analyzing count data.

85 Linking Diabetes and Dementia Risk: A Role for Aβ-42 Induced Activation of the NLRP3 Inflammasome? Results from the ENBIND Study

Abstract Background Midlife Type 2 Diabetes Mellitus (T2DM) is associated with a greater risk of dementia in later life. The innate immune NLRP3 inflammasome, an innate immune receptor, has been implicated in both T2DM and Alzheimer’s Dementia (AD) and can become activated by Amyloid-β 42 (Aβ-42). We analysed inflammasome-dependent cytokine responses in midlife T2DM and correlated these with cognitive and gait performance Methods Peripheral Blood Mononuclear Cells (PBMCs) of otherwise healthy patients with T2DM (n=30; 52 ± 8 yrs) and matched controls (n=15; 52.5 ± 7.86 yrs) were incubated for 18h with the following NLRP3 ligands: (i) Lipopolysaccharide (LPS), (ii) Aβ42 or (ii) LPS & Aβ42. Cell supernatants were analysed for production of the inflammasome-dependent cytokine IL-1β. Cognitive function was assessed using the MoCA and gait speed assessed under self-selected, maximal and cognitive dual-task conditions. Mann-Whitney, Wilcoxon tests and linear regression of log-transformed data were used to analyse results Results Incubation of PBMCs from all participants with NLRP3 agonists was associated with significant production of IL-1β (all p<0.001). There were no statistically significant between-group differences in IL-1β production. MoCA score did not predict IL-1β production by PBMCs. However, poorer performance on the cognitive dual-task gait paradigm was associated with significantly greater IL-1β production in response to LPS & Aβ42 in those with T2DM (p=0.015), which persisted after robust control for demographic, cognitive and cardiovascular covariates (p=0.003). The same association was not seen for healthy controls (p=0.58). Conclusion Both LPS & Aβ42 induce significant IL-1β production in PBMCs which did not differ between those with midlife T2DM and healthy controls. Poorer performance on the cognitive dual task gait paradigm was associated with significantly greater IL-1β production in response to LPS & Aβ42. Given the value of dual task gait in predicting cognitive decline, longitudinal follow up of this cohort may provide insight into the underlying pathophysiological mechanisms and potential biomarkers of dementia risk in T2DM.

Reply: Efficiency and bias of estimators and sampling designs for determining length–weight relationships of fish

The parameters of the allometric equation used to describe the length–weight relationship in fish are usually estimated by linear regression of log-transformed data. Simulation of length–weight reg...

Efficiency and bias of estimators and sampling designs for determining length-weight relationships of fish

The parameters of the allometric equation used to describe the length–weight relationship in fish are usually estimated by linear regression of log-transformed data. Simulation of length–weight regressions showed that for sample sizes commonly encountered in fisheries research, estimates of the intercept are biased high. In contrast with this, estimates of mean weight-at-length are biased low. As a result, different bias-correction factors are necessary to adjust for transformation bias. When the objective is to estimate the intercept of the length–weight equation, two existing methods correct for transformation bias. The appropriate bias-correction factor for mean weight-at-length, however, is exp(σ2/2) where σ2 is the residual variance of the regression. As an alternative to the log-transformation method, the properties of nonlinear least-squares regression were explored. Estimates obtained with nonlinear regression are less efficient, but are relatively robust to departures from the assumed error structure. Simulation of several sampling designs showed that greater precision without loss of accuracy is obtained as subsampling is concentrated toward the extremes of the length distribution.

Effects of nitrogen fertilization and maturity of bromegrass on in situ ruminal digestion kinetics of fiber.

Four ruminally cannulated, nonlactating Holstein cows (593 kg) were fed bromegrass hay diets within a 4 X 4 Latin square. Treatments were arranged factorially and consisted of bromegrass fertilized with 0 or 89 kg N/ha and harvested in the late-boot or full-head stage of maturity. Total tract digestibility of DM (57.6 vs 51.1%), NDF (68.8 vs 63.0%), ADF (51.1 vs 46.0%) and cellulose (63.4 vs 53.5%) decreased with increasing maturity (P less than .05). These forages also were placed in dacron bags for determination of in situ digestion kinetics. Rate, extent of digestion, and lag times were determined for DM and fiber components using linear regression of log-transformed data or a nonlinear fitting procedure. Treatment effects generally were consistent between methods of calculating kinetic data; however, numerical results often differed greatly. Extents of in situ ruminal digestion (72 h residue) for NDF, hemicellulose and cellulose were lower (P less than .05) for full-head than for late-boot-stage bromegrass. Extent of digestion calculated using the nonlinear method followed similar trends. Nitrogen fertilization had no effect on extent or total tract digestibilities of fiber components of DM. In situ disappearance rates (calculated using both methods) for fiber fractions and DM generally were almost always affected less by maturity than by fertilization. Particles of N-fertilized bromegrass had more (P less than .05) bacterial N associated with them during the first 12 h in situ than did particles of unfertilized brome. Surface area equations based on lignification of NDF accurately estimated fiber digestion and suggested that lignification was the primary reason DM and NDF digestibilities decreased with advanced maturity. Due to the relatively low DM intakes of these diets (11 kg/d), rate of passage, not rate of digestion, was of principle importance in determining extent of digestion of these diets.

Computerized curve fitting in the analysis of hydrogen gas clearance curves.

Hydrogen gas clearance curves obtained from the rat gastric corpus were digitized into a computer and then analyzed by three methods: 1) linear regression of log-transformed data, 2) direct curve fitting with a modified Gauss-Newton nonlinear regression algorithm, and 3) Zierler's height-over-area algorithm. For linear regression of log-transformed data, if the initial base-line estimate was inaccurate or normal amounts of experimental noise were present, the log-transformed data was skewed, leading to deviation of the regression line and incorrect estimation of blood flow. By utilization of the direct-fit routine, the initial estimate of the parameters or experimental noise had little influence on the blood flow determination because of iterative improvement of the parameters. In a study of isoproterenol-stimulated gastric blood flow, Zierler's algorithm underestimated the blood flow estimate. We conclude that analysis of hydrogen gas clearance curves by linear regression of log-transformed data or by Zierler's algorithm may potentially introduce errors in blood flow estimates that may be avoided by analysis with a direct-fitting, nonlinear regression algorithm.

ESTIMATING THE ACUTE TOXICITY OF WATERBORNE CHEMICALS IN TROUT FROM MEASUREMENTS OF MEDIAN LETHAL DOSE AND THE OCTANOL-WATER PARTITION COEFFICIENT

Measurements of the median lethal dose (LD50) of chemicals to fish provide a simpler, faster and less expensive alternative to median lethal concentrations (LC50s). Since dose is controlled, LD50s may be a better basis for structure-activity relationships. However, LC50s are used extensively in aquatic hazard assessments. Therefore, LC50s and LD50s for rainbow trout of 48 organic chemicals were measured to determine whether LC50 could be predicted from LD50. A simple linear regression of log-transformed data provided the best fit (r = 0.70), but it accounted for only 50% of the variability in LC50s. LC50s were also strongly correlated with measures of molecular size [molecular weight (MW; r = −0.90) and Parachor (r = −0.89)] and of water-lipid partitioning [octanol-water partition coefficient (Kow; r = −0.73)]. Hence, inclusion of these factors in a multiple regression analysis was examined. Since MW and Parachor were negatively correlated with LD50 (r = −0.61 and −0.60, respectively), they were not true independent variables and were not used. However, there was no relationship of Kow with LD50, and a multiple regression analysis using both LD50 and Kow predicted LC50 with greater certainty (r = 0.92) than did either factor alone. Therefore, LC50 can be predicted from LD50 when partitioning of a chemical from water to lipid is recognized.