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Related Concept Videos

Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
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Observational Learning

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Albert Bandura's observational learning, also known as imitation or modeling, occurs when a person observes and imitates another's behavior. It is a quicker process than operant conditioning. A well-known example is the Bobo doll study, where children who saw an adult acting aggressively towards the doll were more likely to act aggressively when left alone, compared to those who observed a nonaggressive adult. Many psychologists view observational learning as a form of latent learning...
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Data collection refers to a systematic way of obtaining, observing, measuring, and analyzing accurate information. Observational studies are one of the most widely used methods of data collection. It involves collecting data by observing the behavior and physical characteristics of a sample without making any modifications to the sample.
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Assessing the gastrointestinal (GI) system is a complex process that begins with collecting subjective data. This data, collected through patient interviews, provides crucial insights into the patient's health history, perception patterns, and lifestyle habits, all contributing significantly to GI health.
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Learning Subject-Specific Directed Acyclic Graphs With Mixed Effects Structural Equation Models From Observational

Xiang Li1, Shanghong Xie2, Peter McColgan3

  • 1Statistics and Decision Sciences, Janssen Research and Development, LLC, Raritan, NJ, United States.

Frontiers in Genetics
|October 19, 2018
PubMed
Summary
This summary is machine-generated.

We introduce a novel mixed-effects structural equation model (mSEM) to identify causal relationships from observational data. This framework enables precise estimation of subject-specific directed acyclic graphs (DAGs), improving causal discovery.

Keywords:
causal structure discoverygraphical modelsheterogeneitynetwork analysisregularization

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Area of Science:

  • Causal inference
  • Network analysis
  • Statistical modeling

Background:

  • Identifying causal relationships from observational data using directed acyclic graphs (DAGs) is complex.
  • Existing methods struggle with subject-specific heterogeneity and unobserved confounding factors.

Purpose of the Study:

  • To develop a novel framework for estimating subject-specific DAGs from observational data.
  • To improve the identification and precision of causal structure estimation.

Main Methods:

  • Proposed a mixed-effects structural equation model (mSEM) framework.
  • Represented joint distributions using structural causal equations with fixed and random effects.
  • Developed a penalized likelihood approach and a fast, iterative algorithm (DAG-MM) for parameter estimation and sparsity.

Main Results:

  • Theoretically proved the identifiability of the mSEM framework.
  • Demonstrated superior performance compared to existing methods via simulations and protein signaling data analysis.
  • Achieved results consistent with networks derived from interventional data.

Conclusions:

  • The mSEM framework effectively identifies subject-specific causal networks from observational data.
  • Successfully applied the method to identify brain atrophy networks in Huntington's disease patients.
  • The approach offers improved precision and robustness in causal structure discovery.