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JMP 12 Fitting Linear Models

Book Description

JMP 12 Fitting Linear Models focuses on the Fit Model platform and many of its personalities. Linear and logistic regression, analysis of variance and covariance, and stepwise procedures are covered. Also included are multivariate analysis of variance, mixed models, generalized models, and models based on penalized regression techniques.

Table of Contents

  1. Contents
  2. Learn about JMP
    1. Documentation and Additional Resources
    2. Formatting Conventions
    3. JMP Documentation
      1. JMP Documentation Library
      2. Discovering JMP
      3. Using JMP
      4. Basic Analysis
      5. Essential Graphing
      6. Profilers
      7. Design of Experiments Guide
      8. Fitting Linear Models
      9. Specialized Models
      10. Multivariate Methods
      11. Quality and Process Methods
      12. Reliability and Survival Methods
      13. Consumer Research
      14. Scripting Guide
      15. JSL Syntax Reference
      16. JMP Help
    4. Additional Resources for Learning JMP
      1. Tutorials
      2. Sample Data Tables
      3. Learn about Statistical and JSL Terms
      4. Learn JMP Tips and Tricks
      5. Tooltips
      6. JMP User Community
      7. JMPer Cable
      8. JMP Books by Users
      9. The JMP Starter Window
  3. Model Specification
    1. Specify Linear Models
    2. Overview of the Fit Model Platform
    3. Example of a Regression Analysis Using Fit Model
    4. Launch the Fit Model Platform
      1. Fit Model Launch Window Elements
        1. Frequency
        2. Weight
      2. Construct Model Effects
        1. Add
        2. Cross
        3. Nest
        4. Macros
        5. Attributes
        6. Transform
        7. No Intercept
        8. Construct Model Effects Tabs
      3. Fitting Personalities
    5. Model Specification Options
      1. Informative Missing
        1. Continuous Effects
        2. Categorical Effects
        3. Coding Table
    6. Validity Checks
    7. Examples of Model Specifications and Their Model Fits
      1. Simple Linear Regression
      2. Polynomial in X to Degree k
      3. Polynomial in X and Z to Degree k
      4. Multiple Linear Regression
      5. One-Way Analysis of Variance
      6. Two-Way Analysis of Variance
      7. Two-Way Analysis of Variance with Interaction
      8. Three-Way Full Factorial
      9. Analysis of Covariance, Equal Slopes
      10. Analysis of Covariance, Unequal Slopes
      11. Two-Factor Nested Random Effects Model
      12. Three-Factor Fully Nested Random Effects Model
      13. Simple Split Plot or Repeated Measures Model
      14. Two-Factor Response Surface Model
      15. Knotted Spline Effect
  4. Standard Least Squares Report and Options
    1. Analyze Common Classes of Models
    2. Example Using Standard Least Squares
    3. Launch the Standard Least Squares Personality
      1. Fit Model Launch Window
        1. Fixed Effects Only
        2. Random Effects
      2. Standard Least Squares Options in the Fit Model Launch Window
        1. Emphasis Options for Standard Least Squares
      3. Missing Values
    4. Fit Least Squares Report
      1. Single versus Multiple Responses
      2. Report Structure Related to Emphasis
      3. Special Reports
        1. Singularity Details
        2. Response Surface Report
        3. Mixed and Random Effect Model Reports
      4. Least Squares Fit Options
      5. Fit Group Options
    5. Response Options
    6. Regression Reports
      1. Summary of Fit
      2. Analysis of Variance
      3. Parameter Estimates
      4. Effect Tests
      5. Effect Details
        1. Table of Effect Options
        2. LSMeans Table
        3. LSMeans Plot
        4. LSMeans Contrast
        5. LSMeans Student’s t and LSMeans Tukey HSD
        6. LSMeans Dunnett
        7. Test Slices
        8. Power Analysis
      6. Lack of Fit
    7. Estimates
      1. Show Prediction Expression
      2. Sorted Estimates
        1. Sorted Estimates Report for Saturated Models
      3. Expanded Estimates
        1. Interpretation of Tests for Expanded Estimates
      4. Indicator Parameterization Estimates
      5. Sequential Tests
      6. Custom Test
        1. Custom Test Report Components
        2. Custom Test Report Options
      7. Multiple Comparisons
        1. Launch the Option
        2. Comparisons with Overall Average
        3. Comparisons with Control
        4. All Pairwise Comparisons
      8. Joint Factor Tests
      9. Inverse Prediction
      10. Cox Mixtures
      11. Parameter Power
      12. Correlation of Estimates
      13. Coding for Nominal Effects
    8. Effect Screening
      1. Scaled Estimates and the Coding of Continuous Terms
      2. Plot Options
        1. Transformations
        2. Lenth PSE Values
        3. Parameter Estimate Population Report
        4. Correlations of Estimates Report
        5. “Transformation to make uncorrelated” Report
      3. Normal Plot Report
      4. Bayes Plot Report
      5. Pareto Plot Report
    9. Factor Profiling
      1. Profiler
      2. Interaction Plots
      3. Contour Profiler
      4. Mixture Profiler
      5. Cube Plots
      6. Box Cox Y Transformation
      7. Surface Profiler
    10. Row Diagnostics
      1. Leverage Plots
        1. Construction
        2. Confidence Curves
        3. X Axis Scaling
        4. Leverage
        5. Multicollinearity
        6. The Whole Model Actual by Predicted Plot
      2. Press
    11. Save Columns
      1. Prediction Formula
    12. Effect Summary Report
      1. Effect Summary Table Columns
      2. Effect Summary Table Options
      3. Effect Heredity
      4. Multiple Responses
    13. Mixed and Random Effect Model Reports and Options
      1. Mixed Models and Random Effect Models
        1. Random Effects
        2. The Classical Linear Mixed Model
        3. REML versus EMS for Fitting Models with Random Effects
        4. Specifying Random Effects and Fitting Method
        5. Unrestricted Parameterization for Variance Components
        6. Negative Variances
      2. Restricted Maximum Likelihood (REML) Method
        1. Random Effect Predictions
        2. REML Variance Component Estimates
        3. Covariance Matrix of Variance Components Estimates
        4. Iterations
        5. Fixed Effect Tests
        6. REML Save Columns Options
        7. REML Profiler Option
      3. EMS (Traditional) Model Fit Reports
        1. Expected Mean Squares
        2. Variance Component Estimates
        3. Test Denominator Synthesis
        4. Tests wrt Random Effects
        5. EMS Profiler
    14. Models with Linear Dependencies among Model Terms
      1. Singularity Details
      2. Parameter Estimates Report
      3. Effect Tests Report
      4. Examples
    15. Statistical Details
      1. Emphasis Rules
      2. Details of Custom Test Example
      3. Correlation of Estimates
      4. Leverage Plot Details
        1. Construction
        2. Superimposing a Test on the Leverage Plot
      5. The Kackar-Harville Correction
        1. Degrees of Freedom
      6. Power Analysis
        1. Effect Size
        2. Effect Size and Power
        3. Plot of Power by Sample Size
        4. The Least Significant Number (LSN)
        5. The Least Significant Value (LSV)
        6. Power
        7. The Adjusted Power and Confidence Intervals
        8. Example of Retrospective Power Analysis
        9. Prospective Power Analysis
  5. Standard Least Squares Examples
    1. Analyze Common Classes of Models
    2. One-Way Analysis of Variance Example
    3. Analysis of Covariance with Equal Slopes Example
    4. Analysis of Covariance with Unequal Slopes Example
    5. Response Surface Model Example
    6. Split Plot Design Example
    7. Estimation of Random Effect Parameters Example
    8. Knotted Spline Effect Example
    9. Bayes Plot for Active Factors Example
  6. Stepwise Regression Models
    1. Find a Model Using Variable Selection
    2. Overview of Stepwise Regression
    3. Example Using Stepwise Regression
    4. The Stepwise Report
      1. Stepwise Platform Options
      2. Stepwise Regression Control Panel
        1. Stopping Rule
        2. Direction
        3. Go, Stop, Step Buttons
        4. Rules
        5. Buttons
        6. Statistics
        7. Forward Selection Example
        8. Backward Selection Example
      3. Current Estimates Report
      4. Step History Report
    5. Models with Crossed, Interaction, or Polynomial Terms
      1. Example of the Combine Rule
    6. Models with Nominal and Ordinal Effects
      1. Construction of Hierarchical Terms
      2. Example of a Model with a Nominal Term
        1. Construction of Hierarchical Terms in Example
      3. Example of the Restrict Rule for Hierarchical Terms
    7. Performing Ordinal Logistic Stepwise Regression
      1. Example Using Logistic Stepwise Regression
    8. The All Possible Models Option
      1. Example Using the All Possible Models Option
    9. The Model Averaging Option
      1. Example Using the Model Averaging Option
    10. Using Validation
      1. Validation Set with Two or Three Values
        1. Max Validation RSquare
        2. Validation and Test Set Statistic Definitions
      2. K-Fold Cross Validation
        1. RSquare K-Fold Statistic
        2. Max K-Fold RSquare
  7. Generalized Regression Models
    1. Build Models Using Regularization Techniques
    2. Generalized Regression Overview
    3. Example of Generalized Regression
    4. Launch the Generalized Regression Personality
      1. Distribution
        1. Continuous
        2. Discrete
        3. Zero-Inflated
      2. Model Launch Window
        1. Estimation Method Options
        2. Advanced Controls
        3. Validation Method Options
        4. Early Stopping
        5. Go
    5. Model Fit Reports
      1. Model Summary
        1. Model Description Detail
        2. Model Fit Detail
      2. Estimation Details
      3. Solution Path
      4. Parameter Estimates for Centered and Scaled Predictors
      5. Parameter Estimates for Original Predictors
      6. Effect Tests
    6. Model Fit Options
    7. Generalized Regression Options
    8. Additional Examples of the Generalized Regression Personality
      1. Poisson Generalized Regression
      2. Binomial Generalized Regression
      3. Zero-Inflated Poisson Regression
    9. Statistical Details
      1. Statistical Details for Estimation Methods
        1. Ridge Regression
        2. Lasso Regression
        3. Elastic Net
        4. Adaptive Methods
      2. Statistical Details for Advanced Controls
        1. Grid
      3. Statistical Details for Distributions
  8. Mixed Models
    1. Jointly Model the Mean and Covariance
    2. Overview of the Mixed Model Personality
    3. Example Using Mixed Model
    4. Launch the Mixed Model Personality
      1. Fit Model Launch Window
        1. Fixed Effects Tab
        2. Random Effects Tab
        3. Repeated Structure Tab
    5. The Fit Mixed Report
    6. Model Reports
      1. Fit Statistics
        1. Description of Fit Statistics Report
        2. Convergence Score Test
      2. Random Effects Covariance Parameter Estimates
        1. Confidence Intervals for Variance Components
      3. Fixed Effects Parameter Estimates
      4. Repeated Effects Covariance Parameter Estimates
      5. Random Coefficients
      6. Random Effects Predictions
      7. Fixed Effects Tests
    7. Multiple Comparisons
    8. Marginal Model Inference
      1. Actual by Predicted Plot
      2. Residual Plots
      3. Profilers
    9. Conditional Model Inference
      1. Actual by Conditional Predicted Plot
      2. Conditional Residual Plots
      3. Conditional Profilers
    10. Save Columns
    11. Additional Examples
      1. Repeated Measures Example
      2. Covariance Structure: Unstructured Example
      3. Covariance Structure: Residual Example
      4. Covariance Structure: AR(1) Example
        1. Compare Treatment A and Treatment B
        2. Conduct an Equivalence Test
        3. Regression Model for AR(1) Model Example
      5. Split Plot Example
      6. Spatial Example: Uniformity Trial
        1. Fit a Spatial Structure Model
        2. Fit the Independent Errors Model
        3. Conduct a Likelihood Ratio Test (Optional)
        4. Select the Type of Spatial Covariance
        5. Determine the Type of the Spatial Structure
        6. Compare the Model to Block Designs
      7. Correlated Response Example
        1. Explore the Silane*Sulfur*Characteristic Interaction Using the Surface Profiler
        2. Explore Interactions Using the Profiler
    12. Statistical Details
      1. Convergence Score Test
        1. Score Test
        2. Relative Gradient
      2. Random Coefficient Model
      3. Repeated Measures
        1. Unstructured Covariance Structure
        2. AR(1) Covariance Structure
        3. Compound Symmetry Covariance Structure
      4. Spatial Variability
        1. Relationship to a Semivariogram
      5. The Kackar-Harville Correction
        1. Degrees of Freedom
  9. Multivariate Response Models
    1. Fit Relationships Using MANOVA
    2. Example of a Multiple Response Model
    3. The Manova Report
    4. The Manova Fit Options
    5. Response Specification
      1. Choose Response Options
      2. Custom Test Option
        1. Example of Test Details (Canonical Details)
        2. The Centroid Plot
        3. Save Canonical Scores (Canonical Correlation)
    6. Multivariate Tests
      1. The Extended Multivariate Report
      2. Comparison of Multivariate Tests
      3. Univariate Tests and the Test for Sphericity
        1. Example of Univariate and Sphericity Test
    7. Multivariate Model with Repeated Measures
      1. Repeated Measures Example
    8. Example of a Compound Multivariate Model
    9. Discriminant Analysis
      1. Example of the Save Discrim Option
  10. Loglinear Variance Models
    1. Model the Variance and the Mean of the Response
    2. Overview of the Loglinear Variance Model
      1. Dispersion Effects
      2. Model Specification
      3. Notes
    3. Example Using Loglinear Variance
    4. The Loglinear Report
    5. Loglinear Platform Options
      1. Save Columns
      2. Row Diagnostics
    6. Examining the Residuals
    7. Profiling the Fitted Model
      1. Example of Profiling the Fitted Model
  11. Logistic Regression with Nominal or Ordinal Responses
    1. Fit Models for Categorical Responses
    2. Introduction to Logistic Models
    3. The Logistic Fit Report
      1. Logistic Plot
      2. Iteration History
      3. Whole Model Test
      4. Lack of Fit Test (Goodness of Fit)
      5. Parameter Estimates
      6. Likelihood Ratio Tests
    4. Logistic Fit Platform Options
      1. Plot Options
      2. Likelihood Ratio Tests
      3. Wald Tests for Effects
      4. Confidence Intervals
      5. Odds Ratios (Nominal Responses Only)
        1. Dose Response Example
      6. Inverse Prediction
      7. Save Commands
      8. ROC Curve
        1. Example of an ROC Curve
      9. Lift Curve
      10. Confusion Matrix
      11. Profiler
      12. Model Dialog
      13. Effect Summary
    5. Validation
    6. Example of a Nominal Logistic Model
    7. Example of an Ordinal Logistic Model
    8. Example of a Quadratic Ordinal Logistic Model
    9. Stacking Counts in Multiple Columns
  12. Generalized Linear Models
    1. Fit Data with Nonnormal Response Distributions
    2. Overview of Generalized Linear Models
    3. The Generalized Linear Model Personality
    4. Examples of Generalized Linear Models
      1. Model Selection and Deviance
    5. Examples
      1. Poisson Regression
      2. Poisson Regression with Offset
      3. Normal Regression, Log Link
    6. Platform Commands
  13. References
  14. Statistical Details
    1. Fitting Linear Models
    2. The Response Models
      1. Continuous Responses
        1. Fitting Principle for Continuous Response
        2. Base Model for Continuous Responses
      2. Nominal Responses
        1. Fitting Principle For Nominal Response
        2. Base Model for Nominal Responses
      3. Ordinal Responses
        1. Fitting Principle For Ordinal Response
        2. Base Model
    3. The Factor Models
      1. Continuous Factors
      2. Nominal Factors
        1. Interpretation of Parameters
        2. Interactions and Crossed Effects
        3. Nested Effects
        4. Least Squares Means across Nominal Factors
        5. Effective Hypothesis Tests
        6. Singularities and Missing Cells in Nominal Effects
      3. Ordinal Factors
        1. Ordinal Interactions
        2. Hypothesis Tests for Ordinal Crossed Models
        3. Ordinal Least Squares Means
        4. Singularities and Missing Cells in Ordinal Effects
        5. Example with Missing Cell
    4. Frequencies
    5. The Usual Assumptions
      1. Assumed Model
      2. Relative Significance
      3. Multiple Inferences
      4. Validity Assessment
      5. Alternative Methods
    6. Key Statistical Concepts
      1. Uncertainty, a Unifying Concept
      2. The Two Basic Fitting Machines
        1. Springs
        2. Pressure Cylinders
    7. Likelihood, AICc, and BIC
    8. Power Calculations
      1. Computations for the LSN
      2. Computations for the LSV
      3. Computations for the Power
      4. Computations for the Adjusted Power
    9. Inverse Prediction with Confidence Limits
  15. Index
    1. Fitting Linear Models
    2. Symbols
    3. A
    4. B
    5. C
    6. D
    7. E
    8. F
    9. G
    10. H
    11. I
    12. J
    13. K
    14. L
    15. M
    16. N
    17. O
    18. P
    19. Q
    20. R
    21. S
    22. T
    23. U
    24. V
    25. W-Z