nested model

Examples of nested model in the following topics:

• Comparing Nested Models

  • Multilevel (nested) models are appropriate for research designs where data for participants are organized at more than one level.
  • Multilevel models, or nested models, are statistical models of parameters that vary at more than one level.
  • Multilevel models are particularly appropriate for research designs where data for participants are organized at more than one level (i.e., nested data).
  • Multilevel models have the same assumptions as other major general linear models, but some of the assumptions are modified for the hierarchical nature of the design (i.e., nested data).
  • In organizational psychology research, data from individuals must often be nested within teams or other functional units.

• The F-Test

  • It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled.
  • Exact F-tests mainly arise when the models have been fitted to the data using least squares.
  • The hypothesis that a proposed regression model fits the data well (lack-of-fit sum of squares).
  • The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other.

• 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.

• 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.

• A single-variable model for the Mario Kart data

  • Let's fit a linear regression model with the game's condition as a predictor of auction price.
  • The model may be written as:
  • Interpret the coefficient for the game's condition in the model.
  • So 10.90 means that the model predicts an extra $10.90 for those games that are new versus those that are used.
  • Summary of a linear model for predicting auction price based on game condition.

• Identifying variables in the model that may not be helpful

  • H0 : βi = 0 when the other explanatory variables are included in the model.
  • We might consider removing the stock photo variable from the model.
  • The adjusted R2 may be used as an alternative to p-values for model selection, where a higher adjusted R2 represents a better model fit.
  • For instance, we could compare two models using their adjusted R2 , and the model with the higher adjusted R2 would be preferred.
  • The fit for the full regression model, including the adjusted R2 .

• Stepwise Regression

  • The frequent practice of fitting the final selected model, followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account, has led to calls to stop using stepwise model building altogether -- or to at least make sure model uncertainty is correctly reflected.
  • Forward selection involves starting with no variables in the model, testing the addition of each variable using a chosen model comparison criterion, adding the variable (if any) that improves the model the most, and repeating this process until none improves the model.
  • A way to test for errors in models created by stepwise regression is to not rely on the model's $F$-statistic, significance, or multiple-r, but instead assess the model against a set of data that was not used to create the model.
  • This is often done by building a model based on a sample of the dataset available (e.g., 70%) and use the remaining 30% of the dataset to assess the accuracy of the model.
  • Models that are created may be too-small than the real models in the data.

• Checking model assumptions using graphs

  • "All models are wrong, but some are useful" -George E.P.
  • The truth is that no model is perfect.
  • However, even imperfect models can be useful.
  • Reporting a flawed model can be reasonable so long as we are clear and report the model's shortcomings.
  • This video covers key ideas for evaluating a multiple regression model in the context of the model fit in Sections 8.1 and 8.2.

• The Role of the Model

  • A statistical model is a set of assumptions concerning the generation of the observed data and similar data.
  • A statistical model is a set of assumptions concerning the generation of the observed data and similar data.
  • The family of generalized linear models is a widely used and flexible class of parametric models.
  • More generally, semi-parametric models can often be separated into 'structural' and 'random variation' components.
  • The use of any parametric model is viewed skeptically by most experts in sampling human populations.