Random Coefficient Models

By Nicholas T. Longford. 1994

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Liangjun Su
2. Sun-Joo Cho
3. Xia Wang
4. Sainan Jin
5. L. DeCarlo
6. Wen Luo
7. Oi-man Kwok
8. J. Schoeneberger

Citations in the corpus

• Do energy efficiency policies save energy? A new approach based on energy policy indicators (in the EU Member States) (2020, unknown): “Hsiao and Pesaran (2008) illustrates how panel models may allow for heterogeneous coefficients.”
• Emotion and Reason in Everyday Risk Perception (2011, unknown): “As such, our data can be efficiently modeled using hierarchical (or multi-level) linear models (HLM) (Longford, 1993; Byrk & Raudenbush, 2002).”
• Random Coefficients on Endogenous Variables in Simultaneous Equations Models (2014, background): “See Raj and Ullah (1981, page 9) and Hsiao and Pesaran (2008) for further references and discussion.”
• The Impact of Sample Size and Other Factors When Estimating Multilevel Logistic Models (2016, methodology): “These ML methods have struggled to converge on final solutions due to limited variability when outcome prevalence is extreme (i.e., the proportion of outcome events approaches zero or one) and sample sizes are small (Longford, 1993).”
• Fixed effects and variance components estimation in three‐level meta‐analysis (2011, unknown): “Following Longford (1993), reasonable starting solutions for τ R and the diagonal elements of the variance components matrix Ω(3)R at the third level are functions of the residuals, namely τ 0ð ÞR ¼ 1k∑ k i¼1 e2i and Ω 0ð ÞRj ¼ 1m ∑ m g¼1 eT3;gð ÞZ jð Þ 3;gð Þ 2 ∑ m g¼1 Z jð Þ3;gð Þ T Z jð Þ3;gð…”
• The Consequences of Ignoring Individuals' Mobility in Multilevel Growth Models (2012, methodology): “The covariance matrix of the maximum likelihood estimator of the fixed effects g as in Equation 1 is given by cov(ĝ) 1⁄4 (Z0V (1)Z) 1 (Longford, 1993), where V is the covariance matrix of y and is given by V 1⁄4 XGX0 þ R, where”
• A Multilevel Mixture IRT Model With an Application to DIF (2010, methodology): “Multilevel models, also known as hierarchical linear models (HLM), allow the natural multilevel structure of educational and psychological data to be represented formally in the analysis (Bryk & Raudenbush, 1992; Goldstein, 1987; Longford, 1993).”
• On the statistical and theoretical basis of signal detection theory and extensions: Unequal variance, random coefficient, and mixture models (2010, background): “(9) is a probit model with a slope, d + γ , that varies over trials, and is an example of what is known as a random coefficient model in statistics (e.g. Longford, 1993), because the coefficient d+ γ is a random variable, rather than a fixed constant d.”