目录：
1 A First Tour Through R by Example  . . . . . . . . . . . . . . . . . 1
1.1 Getting Started   . . . . . . . . . . . . . . . . 1
1.2 The Experiment of Hecht, Shlaer and Pirenne  . . . 2
1.2.1 Accessing the Data Set  . . . . . . . . . . . . . . . . . . . 2
1.2.2 Viewing the Data Set   5
1.2.3 One More Plot Before Modeling  . . . . . . . . 7
1.3 Modeling the Data   . . . . . . . . . . . . 8
1.3.1 Modeling a Subset of the Data  . . . . . . . . . . . 10
1.3.2 Estimating Thresholds and jnd’s  . . . . . . . . . 15
1.3.3 Modeling All of the Data . . . . . . . . . . . . . . . . . 16
1.3.4 Odds and Ends   . . . . . . . 19
1.4 Exercises .   20
2 Modeling in R    . 21
2.1 Introduction .  . . . . . . . . . . . . . . . . . . 21
2.2 The Linear Model   . . . . . . . . . . . . 21
2.2.1 Development of First- and Second-OrderMotion . . . . . . . . . . . 26
2.3 Linear Mixed-EffectsModels  . . . . . . . . . . . . . . . . . . . . 32
2.3.1 The ModelFest Data Set . . . . . . . . . . . . . . . . . . 33
2.4 Nonlinear Models   . . . . . . . . . . . . 44
2.4.1 Chromatic Sensitivity Across the Life Span . . . . . . . . . . . . . . . . . 45
2.5 Additive Models .  . . . . . . . . . . . . . 49
2.5.1 Chromatic Sensitivity, Again  . . . . . . . . . . . . 50
2.6 Generalized Linear Models   . . 53
2.6.1 Chromatic Sensitivity, Yet Again  . . . . . . . . 54
2.7 Which Model to Choose?   . . . . 56
2.8 Exercises .   57
3 Signal Detection Theory   . . . . . . . . . . . 61
3.1 Introduction .  . . . . . . . . . . . . . . . . . . 61
3.2 Sensory and Decision Spaces   61
3.2.1 Optimal Detection   . . . 63
3.3 Case 1: Equal-Variance Gaussian SDT  . . . . . . . . . . 64
3.3.1 The Decision Rule for Equal-Variance Gaussian SDT . . . . . . 66
3.3.2 Simulating and Fitting Equal-Variance Gaussian SDT . . . . . . 66
3.3.3 Maximum Likelihood Estimation of Equal-Variance
Gaussian SDT Parameters . . . . . . . . . . . . . . . . 68
3.3.4 Fisher’s Tea Test   . . . . . 69
3.3.5 Fitting Equal-Variance SDT as a GLM . . 72
3.3.6 Fitting with Multiple Conditions  . . . . . . . . 74
3.3.7 Complete Separation   77
3.3.8 The Receiver Operating Characteristic  . . 79
3.4 Case 2: Unequal-Variance Gaussian SDT  . . . . . . . . 81
3.4.1 The Decision Rule for Unequal-Variance
Gaussian SDT  . . . . . . . . 81
3.4.2 Simulating Unequal-Variance Gaussian SDT . . . . . . . . . . . . . . . . 82
3.4.3 Fitting Unequal-Variance Gaussian SDT
by Direct Optimization . . . . . . . . . . . . . . . . . . . 85
3.5 Case 3: Exponential SDT   . . . . 88
3.6 m-Alternative Forced-Choice and Other Paradigms .. . . . . . . . . . . . . . . . . 89
3.6.1 Letter Identification: 4AFC  . . . . . . . . . . . . . . 90
3.6.2 d’ for Other Paradigms  . . . . . . . . . . . . . . . . . . . 91
3.7 Rating Scales   . . . . . . . . . . . . . . . . . 91
3.7.1 Ordinal Regression Models on Cumulative Probabilities . . . 94
3.7.2 Sensitivity to Family Resemblance  . . . . . . 99
4 The Psychometric Function: Introduction  . . . . . . . . . . 107
4.1 Brief Historical Review   . . . . . . 107
4.2 Fitting Psychometric Functions to Data  . . . . . . . . . . 113
4.2.1 Direct Maximization of Likelihood. . . . . . 114
4.3 A Model Psychophysical Observer . . . . . . . . . . . . . . . 120
4.4 Fitting Psychometric Functions with glm  . . . . . . . 121
4.4.1 Alignment Judgments of Drifting Grating Pairs . . . . . . . . . . . . . 123
4.4.2 Selecting Models and Analysis of Deviance . . . . . . . . . . . . . . . . . 126
4.5 Diagnostic Plots   . . . . . . . . . . . . . . 129
4.6 Complete Separation   . . . . . . . . . 135
4.7 The Fitted Model   . . . . . . . . . . . . . 136
4.8 Summary .   138
5 The Psychometric Function: Continuation  . . . . . . . . . . 141
5.1 Fitting Multiple-Alternative Forced Choice Data Sets. . . . . . . . . . . . . . . . 141
5.1.1 Using an Offset to Set the Lower Asymptote . . . . . . . . . . . . . . . . 142
5.1.2 Using Specialized Link Functions to Set the
Lower Asymptote  . . . . 145
5.1.3 Estimating Upper and Lower Asymptotes . . . . . . . . . . . . . . . . . . . 147
5.2 Staircase Methods   . . . . . . . . . . . . 151
5.3 Extracting Fitted Parameters .  153
5.4 Methods for Standard Errors and Confidence Intervals . . . . . . . . . . . . . . 155
5.5 Bootstrap Standard Error Estimates  . . . . . . . . . . . . . . 157
5.6 Nonparametric Approaches   . 163
6 Classification Images   . . . . . . . . . . . . . . 167
6.1 Ahumada’s Experiment   . . . . . . 167
6.1.1 Simulating a Classification Image Experiment . . . . . . . . . . . . . . 169
6.1.2 The Information Used in Offset Detection . . . . . . . . . . . . . . . . . . 172
6.2 Some History   . . . . . . . . . . . . . . . . . 174
6.3 The Classification Image as a Linear Model  . . . . . 175
6.3.1 Detection of a Gabor Temporal Modulation . . . . . . . . . . . . . . . . . 175
6.3.2 Estimation by a Linear Model  . . . . . . . . . . . 177
6.3.3 Estimation with lm   . . 177
6.3.4 Model Evaluation .  . . . 178
6.4 Classification Image Estimation with glm  . . . . . . . 179
6.5 Fitting a Smooth Model   . . . . . 183
6.5.1 Higher-Order Classification Images  . . . . . 187
6.6 Comparing Methods.  . . . . . . . . . 188
7 Maximum Likelihood Difference Scaling  . . . . . . . . . . . . 195
7.1 Introduction .  . . . . . . . . . . . . . . . . . . 195
7.1.1 Choosing the Quadruples  . . . . . . . . . . . . . . . . 199
7.1.2 Data Format .  . . . . . . . . . 200
7.1.3 Fitting the Model: Direct Maximization . 201
7.1.4 GLM Method   . . . . . . . . 203
7.1.5 Representation as a Ratio Scale  . . . . . . . . . . 205
7.2 Perception of Correlation in Scatterplots  . . . . . . . . 205
7.2.1 Estimating a Difference Scale . . . . . . . . . . . . 207
7.2.2 Fitting a Parametric Difference Scale  . . . 209
7.2.3 Visualizing the Decision Space for Difference Judgments . . 211
7.3 The Method of Triads   . . . . . . . . 214
7.4 The Effect of Number of Trials  . . . . . . . . . . . . . . . . . . . 215
7.5 Bootstrap Standard Errors  . . . . 217
7.6 Robustness and Diagnostic Tests  . . . . . . . . . . . . . . . . . 219
7.6.1 Goodness of Fit   . . . . . . 219
7.6.2 Diagnostic Test of the MeasurementModel. . . . . . . . . . . . . . . . . . 223
8 Maximum Likelihood ConjointMeasurement  . . . . . . 229
8.1 Introduction   . . . . . . . . . . . . . . . . . . 229
8.2 The Model   . . . . . . . . . . . . . . . . . . . . 233
8.3 The Nonparametric Model   . . . 236
8.3.1 Fitting the Nonparametric Model Directly
by Maximum Likelihood . . . . . . . . . . . . . . . . . 240
8.3.2 Fitting the Nonparametric Model with glm . . . . . . . . . . . . . . . . . . 241
8.4 Fitting Parametric Models   . . . 249
8.5 Resampling Methods   . . . . . . . . 252
8.5.1 The Choice of Stimuli  . . . . . . . . . . . . . . . . . . . . 252
8.6 The Axiomatic Model   . . . . . . . 254
9 Mixed-Effects Models   . . . . . . . . . . . . . 257
9.1 Simple Detection   . . . . . . . . . . . . . 259
9.1.1 Random Criterion Effects  . . . . . . . . . . . . . . . . 259
9.1.2 Random Sensitivity Effects  . . . . . . . . . . . . . . 263
9.2 Rating Scale Data  . . . . . . . . . . . . . 264
9.3 Psychometric Functions: Random Intercepts and Slopes. . . . . . . . . . . . . 267
9.3.1 Context Effects on Detection  . . . . . . . . . . . . 276
9.3.2 Multiple-Alternative Forced-Choice Data . . . . . . . . . . . . . . . . . . . . 286
9.4 MLDS    . . . . 287
9.4.1 Regression on the Decision Variable: Fixed
Functional Form   . . . . . 287
9.4.2 Regression on the Decision Variable: Rescaling
to a Common Scale   . . 290
9.4.3 Regression on the Estimated Coefficients . . . . . . . . . . . . . . . . . . . . 295
9.5 Whither from Here   . . . . . . . . . . . 301
A Some Basics of R   . . . . . . . . . . . . . . . . . . 303
A.1 Installing R   . . . . . . . . . . . . . . . . . . . 303
A.2 Basic Data Types   . . . . . . . . . . . . . 304
A.2.1 Vectors   . . . . . . . . . . . . . . . 304
A.2.2 Factors   . . . . . . . . . . . . . . . 309
A.2.3 Lists   . . . . . . . . . . . . . . . . . . 310
A.2.4 Data Frames  . . . . . . . . . . 311
A.2.5 Other Types of Objects  . . . . . . . . . . . . . . . . . . 313
A.3 Simple Programming Constructs  . . . . . . . . . . . . . . . . . 313
A.4 Interacting with the Operating System  . . . . . . . . . . . 313
A.5 Getting Data into and Out of R  . . . . . . . . . . . . . . . . . . . 314
A.5.1 Writing and Reading Text Files  . . . . . . . . . 315
A.5.2 write.table.  . . . . . . . 315
A.5.3 read.table   . . . . . . . . . 315
A.5.4 scan .  . . . . . . . . . . . . . . . . . 317
A.5.5 save and load.  . . . . . . 317
A.5.6 Interacting with Matlab  . . . . . . . . . . . . . . . . . . 318
A.5.7 Interacting with Excel Files  . . . . . . . . . . . . . 318
A.5.8 Reading in Other Formats  . . . . . . . . . . . . . . . . 318
B Statistical Background   . . . . . . . . . . . . 321
B.1 Introduction .  . . . . . . . . . . . . . . . . . . 321
B.2 Random Variables and Monte Carlo Methods  . . . 323
B.2.1 Finite, Discrete Random Variables  . . . . . . 323
B.2.2 Bernoulli Random Variables  . . . . . . . . . . . . . 324
B.2.3 Continuous Random Variables  . . . . . . . . . . . 324
B.2.4 Discrete vs Continuous Random Variables .. . . . . . . . . . . . . . . . . . 325
B.2.5 Normal (Gaussian) Random Variables  . . 326
B.2.6 Location-Scale Families  . . . . . . . . . . . . . . . . . . 327
B.3 Independence and Samples   . . 328
B.3.1 Expectation and Moments . . . . . . . . . . . . . . . . 329
B.3.2 Bernoulli and Binomial Random Variables . . . . . . . . . . . . . . . . . . 331
B.3.3 Uniform Random Variables  . . . . . . . . . . . . . . 331
B.3.4 Exponential and Gamma Random Variables . . . . . . . . . . . . . . . . . 333
B.3.5 The Exponential Family  . . . . . . . . . . . . . . . . . . 333
B.3.6 Monte Carlo Methods  . . . . . . . . . . . . . . . . . . . . 335
B.4 Estimation   . . . . . . . . . . . . . . . . . . . . 335
B.4.1 What Makes an Estimate “Good”?  . . . . . . 336
B.4.2 Maximum Likelihood Estimation . . . . . . . . 337
B.4.3 Why Likelihood? Some Properties  . . . . . . 340
B.4.4 Bayesian Estimation   . 342
B.5 Nested Hypothesis Testing   . . . 347
B.5.1 Reparameterization: Nested Hypothesis Tests . . . . . . . . . . . . . . . 349
B.5.2 The Akaike Information Criterion  . . . . . . . 349
References   . . . . . . . . . . 351
Index    . . . . . . . . . . . . . . . . 361

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