ANCOVA model

Examples of ANCOVA model in the following topics:

• Models with Both Quantitative and Qualitative Variables

  • A regression model that contains a mixture of quantitative and qualitative variables is called an Analysis of Covariance (ANCOVA) model.
  • A regression model that contains a mixture of both quantitative and qualitative variables is called an Analysis of Covariance (ANCOVA) model.
  • ANCOVA models are extensions of ANOVA models.
  • Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.
  • To see if the CV significantly interacts with the IV, run an ANCOVA model including both the IV and the CVxIV interaction term.

• Two Regression Lines

  • Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.
  • Therefore, when performing ANCOVA, we are adjusting the DV means to what they would be if all groups were equal on the CV.
  • Another use of ANCOVA is to adjust for preexisting differences in nonequivalent (intact) groups.
  • There are five assumptions that underlie the use of ANCOVA and affect interpretation of the results:
  • This pie chart shows the partitioning of variance within ANCOVA analysis.

• Comparing Nested Models

  • Multilevel models, or nested models, are statistical models of parameters that vary at more than one level.
  • These models can be seen as generalizations of linear models (in particular, linear regression); although, they can also extend to non-linear models.
  • Furthermore, multilevel models can be used as an alternative to analysis of covariance (ANCOVA), where scores on the dependent variable are adjusted for covariates (i.e., individual differences) before testing treatment differences.
  • Multilevel models are able to analyze these experiments without the assumptions of homogeneity-of-regression slopes that is required by ANCOVA.
  • Random slopes model.

• Economic Models

  • A model is simply a framework that is designed to show complex economic processes.
  • Economists use models in order to study and portray situations.
  • Models are based on theory and follow the rules of deductive logic.
  • However, creating a model does have two basic steps: 1) generate the model, and 2) checking the model for accuracy - also known as diagnostics.
  • Some economic models also use qualitative analysis.

• Modeling Ecosystem Dynamics

  • Conceptual models describe ecosystem structure, while analytical and simulation models use algorithms to predict ecosystem dynamics.
  • Conceptual models are usually depicted graphically as flow charts.
  • These diagrams are sometimes called compartment models.
  • Like analytical models, simulation models use complex algorithms to predict ecosystem dynamics.
  • These kinds of models tend to be more widely used.

• Introduction to Model selection

  • The best model is not always the most complicated.
  • In this section we discuss model selection strategies, which will help us eliminate from the model variables that are less important.
  • In this section, and in practice, the model that includes all available explanatory variables is often referred to as the full model.
  • Our goal is to assess whether the full model is the best model.
  • If it isn't, we want to identify a smaller model that is preferable.

• Essential Functions for Mathematical Modeling

  • The process of developing a mathematical model is termed mathematical modeling.
  • Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models.
  • These and other types of models can overlap, with a given model involving a variety of abstract structures.
  • In general, mathematical models may include logical models, as far as logic is taken as a part of mathematics.
  • For example, a simple model of population growth is the Malthusian growth model.

• Fama-French Three-Factor Model

  • The Fama–French three-factor model is a linear model designed by Eugene Fama and Kenneth French to describe stock returns.
  • The Fama–French three-factor model is a model designed by Eugene Fama and Kenneth French to describe stock returns .
  • Like CAPM and the Arbitrage Pricing Theory, the Fama-French three-factor model is a linear model that relates structural factors to the expected return of an asset.
  • Unlike those two models, however, the Fama-French model has three specific and defined factors.
  • Though it is more complex than CAPM, the Fama-French model has been shown to be a better at explaining the returns of a diversified portfolio: CAPM explains 70% of returns on average, while the Fama-French model explains 90% on average.

• Two model selection strategies

  • If one of these smaller models has a higher adjusted R2 than our current model, we pick the smaller model with the largest adjusted R2.
  • That is, we fit the model including just the cond new predictor, then the model including just the stock photo variable, then a model with just duration, and a model with just wheels.
  • Each of the four models (yes, we fit four models!
  • We fit three new models:
  • If one of these models has a larger than the model with no variables, we use this new model.

• Model selection exercises

  • Determine if any other variable(s) should be removed from the model.
  • Determine if any other variable(s) should be removed from the model.
  • Based on this table, which variable should be added to the model first?
  • Based on this table, which variable should be added to the model first?
  • We should consider removing this variable from the model.