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Related Concept Videos

Weighted Mean00:57

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
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Variation01:19

Variation

An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
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Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Regression Toward the Mean01:52

Regression Toward the Mean

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Related Experiment Video

Updated: Jun 3, 2026

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index
06:55

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

Weighted scores method for regression models with dependent data.

Aristidis K Nikoloulopoulos1, Harry Joe, N Rao Chaganty

  • 1School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK. a.nikoloulopoulos@uea.ac.uk

Biostatistics (Oxford, England)
|March 26, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a weighted scores method for analyzing dependent data in regression models, offering a robust and efficient alternative to complex copula methods when dependence is not the primary focus. The new approach provides nearly maximum likelihood efficiency for analyzing health care utilization.

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Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
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Last Updated: Jun 3, 2026

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index
06:55

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Published on: January 8, 2020

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
06:33

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Published on: October 11, 2018

Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Health Services Research

Background:

  • Existing copula-based models for dependent data (e.g., clustered, longitudinal overdispersed counts) offer straightforward estimation but can be complex when dependence is not the primary interest.
  • Regression analysis with dependent data often requires specialized models that account for complex correlation structures.

Purpose of the Study:

  • To propose and evaluate a novel "weighted scores method" for regression analysis of dependent data.
  • To provide a method that focuses on univariate regression parameters while effectively handling data dependence.
  • To assess the robustness and efficiency of the proposed method compared to existing approaches.

Main Methods:

  • The weighted scores method involves weighting score functions of univariate margins.
  • Weight matrices are derived from fitting a discretized multivariate normal distribution to capture dependence.
  • The methodology is applied to negative binomial regression models for overdispersed count data.

Main Results:

  • Asymptotic and small-sample efficiency calculations demonstrate the robustness of the weighted scores method.
  • The proposed method achieves efficiency comparable to maximum likelihood estimation in fully specified copula models.
  • The method is effective for analyzing health care utilization data based on family characteristics.

Conclusions:

  • The weighted scores method offers a practical and efficient alternative for regression with dependent data when the focus is on marginal parameters.
  • This approach simplifies analysis without sacrificing significant statistical efficiency.
  • The method is applicable to real-world health services research, as shown in the healthcare utilization example.