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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Functional Classification of Joints
The functional classification of joints is determined by the amount of mobility between the adjacent bones. Joints are functionally classified as a synarthrosis or immobile joint, an amphiarthrosis or slightly moveable joint, or as a diarthrosis, a freely moveable joint. Fibrous and cartilaginous joints can be functionally classified as either synarthroses  or amphiarthroses, whereas all synovial joints are classified as diarthroses.
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Multiple-membership multiple-classification models for social network and group dependences.

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Summary
This summary is machine-generated.

This study introduces a new statistical model to analyze how social networks, school, and living area influence educational attainment. Ignoring social networks significantly impacts estimates of variation and regression coefficients.

Keywords:
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Area of Science:

  • Social Sciences
  • Statistics
  • Education

Background:

  • Traditional social network analysis often overlooks group-level factors like school or neighborhood.
  • Multilevel modeling typically ignores the influence of social networks on individual outcomes.
  • A gap exists in jointly analyzing social network and group-based dependencies.

Purpose of the Study:

  • To bridge the divide between social network and multilevel modeling literature.
  • To present a novel modeling approach for investigating joint social network and group dependencies.
  • To compare the influence of social networks versus school and area on individual responses.

Main Methods:

  • Developed a multiple-membership, multiple-classification modeling approach.
  • Applied the model to a subsample of the Adolescent Health Study data.
  • Analyzed educational attainment as the response variable, considering sex, ethnicity, and age as covariates.
  • Incorporated individual, network, school, and area dependencies into the analysis.

Main Results:

  • Ignoring social networks alters estimates of variation for individual, school, and area factors.
  • Social network analysis influences point estimates and standard errors of regression coefficients.
  • The model successfully accounts for various network configurations like ego-nets and cliques.

Conclusions:

  • The proposed approach offers a flexible and practical method for studying social network influences on individual outcomes.
  • It enables the estimation of variation shares attributable to networks, schools, and areas.
  • This integrated approach provides a more comprehensive understanding of factors affecting educational attainment.