Plane Answers to Complex Questions

Christensen, Ronald

doi:10.1007/978-0-387-21544-0

Cited by 113 publications

(36 citation statements)

References 54 publications

(67 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is straightforward to show that the least squares and maximum likelihood solutions to this equation are given by β = (X T X) −1 X T Y and Var(β) = (X T X) −1 σ 2 (Christensen, 2002). Notably, in the case that the columns of X are highly correlated, X T X will be singular and we replace (X T X) −1 with (X T X) − where '−' denotes generalized inverse, and a unique solution to Equation 1 does not exist.…”

Section: Ridge Regressionmentioning

confidence: 99%

Ridge Regression for Longitudinal Biomarker Data

Eliot

Ferguson²,

Reilly³

et al. 2011

The International Journal of Biostatistics

View full text Add to dashboard Cite

Technological advances facilitating the acquisition of large arrays of biomarker data have led to new opportunities to understand and characterize disease progression over time. This creates an analytical challenge, however, due to the large numbers of potentially informative markers, the high degrees of correlation among them, and the time-dependent trajectories of association. We propose a mixed ridge estimator, which integrates ridge regression into the mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. An expectation-maximization algorithm is described to account for unknown variance and covariance parameters. Model performance is demonstrated through a simulation study and an application of the mixed ridge approach to data arising from a study of cardiometabolic biomarker responses to evoked inflammation induced by experimental low-dose endotoxemia.

show abstract

Section: Ridge Regressionmentioning

confidence: 99%

Ridge Regression for Longitudinal Biomarker Data

Eliot

Ferguson²,

Reilly³

et al. 2011

The International Journal of Biostatistics

View full text Add to dashboard Cite

show abstract

“…The temporal relationship was determined using linear regression. The assumption in linear regression is that the n observations of increase in dose rate, H, at a certain location can be described by the following linear model (Christensen, 1996):…”

Section: Relating Dose Rate To Rainfall Intensitymentioning

confidence: 99%

“…We compared ordinary kriging (OK) to universal kriging (UK) (Chilès and Delfiner, 1999;Christensen, 1996) to determine whether including a spatial trend improved the accuracy of the interpolated map. Note that in contrast to section 2.4, the trend is fitted in space and not in time.…”

Section: Mapping Dose Rate With-and Without Trendmentioning

confidence: 99%

“…The third measure is the Mean Kriging Variance (MKV) defined as the mean of the kriging variance calculated for each prediction location (Christensen, 1996).…”

Section: Quantifying the Accuracy Of The Mapmentioning

confidence: 99%

“…Hiemstra et al (2009) focused on the interpolation of dose rate in non-emergency, background situations, providing a first step towards an interpolation system suitable for emergency situations. In addition, Hiemstra et al (2009) suggested to use trend information in a universal kriging (UK) approach (Chilès and Delfiner, 1999;Christensen, 1996), using soil type to improve the interpolated map. Many other studies (Knotters et al, 1995;Bishop and McBratney, 2001;Bourennane and King, 2003;Lloyd, 2005;Yemefack et al, 2005;Hengl et al, 2007) showed that accounting for a trend can improve an interpolated map.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Using rainfall radar data to improve interpolated maps of dose rate in the Netherlands

Hiemstra

Pebesma

Heuvelink

et al. 2010

Science of The Total Environment

View full text Add to dashboard Cite

Logistic Regression

Christensen

2005

Encyclopedia of Statistics in Behavioral Science

View full text Add to dashboard Cite

Logistic regression is a method for predicting the outcomes of ‘either‐or’ trials. Either‐or trials occur frequently in research. A person responds appropriately to a drug or does not; the dose of the drug may affect the outcome. A person may support a political party or not; the response may be related to their income. A person may have a heart attack in a 10‐year period; the response may be related to age, weight, blood pressure, or cholesterol. We discuss basic ideas of modeling in the section titled ‘Basic Ideas’ and basic ideas of data analysis in the section titled ‘Fundamental Data Analysis’. Subsequent sections examine model testing, variable selection, outliers and influential observations, methods for testing lack of fit, exact conditional inference, random effects, and Bayesian analysis.

show abstract

Plane Answers to Complex Questions

Cited by 113 publications

References 54 publications

Ridge Regression for Longitudinal Biomarker Data

Ridge Regression for Longitudinal Biomarker Data

Using rainfall radar data to improve interpolated maps of dose rate in the Netherlands

Logistic Regression

Contact Info

Product

Resources

About