Readings for MTH207
Preface
FOUNDATIONS
1
Model Types & Methods
1.1
Distinguishing Methods
1.2
Method Purposes
2
2-Sample t Review
2.1
Review
2.2
Analysis in R
2.3
Signal-to-Noise
3
Model Concepts
3.1
What is a Model
3.2
Assessing Fit (SS)
3.3
Residual Degrees-of-Freedom
3.4
Mean-Squares
4
Model Comparison
4.1
Competing Models
4.2
Measuring Increase in Fit
4.3
Measuring Increase in Complexity
4.4
“Noise” Variances
4.5
“Signal” Variance (Benefit-to-Cost)
4.6
Ratio of Variances (Signal-to-Noise)
4.7
ANOVA Table
4.8
Two-Sample t-Test Revisited: Using Linear Models
4.9
One More Look at MS and F-test
ONE-WAY ANOVA
5
One-Way Foundations
5.1
Analytical Foundation
5.2
One-Way ANOVA in R
6
One-Way Multiple Comparisons
6.1
Multiple Comparison Problem
6.2
Correction Methods
6.3
Multiple Comparisons in R
7
One-Way Assumptions
7.1
Independence
7.2
Equal Variances
7.3
Normality
7.4
No Outliers
7.5
Testing Assumptions in R
8
One-Way Transformations
8.1
Power Transformations
8.2
Transformations from Theory
8.3
Interpretations After Transformations
8.4
Back-Transformations in R
9
One-Way Summary
9.1
Suggested Workflow
9.2
Nematodes (
No Transformation
)
9.3
Ant Foraging (
Transformation
)
9.4
Peak Discharge (
Transformation
)
TWO-WAY ANOVA
10
Two-Way Conceptual Foundation
10.1
Two Factors
10.2
Interaction Effects
10.3
Main Effects
10.4
Advantages of CCFD
11
Two-Way Analytical Foundation
11.1
Terminology
11.2
Models
11.3
SS
Total
, df
Total
, and MS
Total
11.4
SS
Within
, df
Within
, and MS
Within
11.5
SS
Among
, df
Among
, and MS
Among
11.6
Partitioning SS
Among
11.7
ANOVA Table
12
Two-Way Analysis
12.1
Model Fitting in R
12.2
Assumptions
12.3
Main and Interaction Effects (ANOVA Table)
12.4
Multiple Comparisons
12.5
Graphing Results
13
Two-Way Summary
13.1
Suggested Workflow
13.2
Expected Prices (
No Transformation
)
13.3
Blood Pressure (
No Transformation
)
13.4
Crayfish Foraging (
Transformation
)
SIMPLE LINEAR REGRESSION
14
SLR Foundational Principles
14.1
Equation of a Line
14.2
Best-Fit Line
14.3
Best-Fit Line in R
15
SLR Inference
15.1
Variability Around the Line
15.2
Slope
15.3
Intercept
15.4
Slope and Intercept in R
15.5
Predicting Means
15.6
Predicting Individuals
15.7
Predictions in R
16
SLR Models
16.1
Models
16.2
ANOVA Table
16.3
Coefficient Of Determination
17
SLR Assumptions
17.1
Residual Plot
17.2
Independence
17.3
Homoscedasticity
17.4
Normality
17.5
No Outliers or Influential Points
17.6
Linearity
17.7
Testing Assumptions in R
18
SLR Transformations
18.1
Transformations from Theoretical Relationships
18.2
Trial-and-Error Method
18.3
Back-Transformation in SLR
18.4
Examples
19
SLR Summary
19.1
Suggested Workflow
19.2
Climate Change Data (
No Transformation
)
19.3
Forest Allometrics (Transformation)
INDICATOR VARIABLE REGRESSION
20
IVR Variables
20.1
Indicator Variables
20.2
Interaction Variables
21
IVR Models & Sub-Models
21.1
Ultimate Full Model
21.2
Sub-Models
21.3
Interpreting Parameter Estimates
21.4
Ultimate Full Model in R
22
IVR Testing
22.1
F-ratio Test Statistic
22.2
Parallel Lines Test
22.3
Coincident Lines Test
22.4
Relationship Test
22.5
All Tests in R
22.6
More Groups (Different Slopes)
22.7
More Groups (Same Slopes)
23
IVR Analysis
23.1
Assumptions & Transformations
23.2
Multiple Comparisons for Slopes
23.3
Multiple Comparisons for Intercepts
24
IVR Summary
24.1
Suggested Workflow
24.2
Fish Energy Density (
No Transformation
)
24.3
Shrub Allometry (
Transformation
)
LOGISTIC REGRESSION
25
Foundational Principles
25.1
Need for a Transformation
25.2
Odds
25.3
Log Odds and the Logit Transformation
25.4
Back-Transformation Introduction
26
Models and Predictions
26.1
Slope & Back-Transformed Slope
26.2
Back-Transformed Slope
26.3
Predictions
26.4
“Reverse” Predictions
26.5
Another Example
26.6
Variability Estimates
27
Analysis
27.1
Data Preparation
27.2
Fitting the Model
27.3
Relationship Test
27.4
Parameter Estimates
27.5
Predictions
27.6
Plotting Best-Fit Line
28
Logistic Regression Summary
28.1
Suggested Workflow
28.2
Slimy Salamander Occurrence
Appendix – R Generic Code
Common Codes
Foundations
One-Way ANOVA
Two-Way ANOVA
Simple Linear Regression
Indicator Variable Regression
Logistic Regression
References
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Readings for MTH207
References