Sas(R) for Monte Carlo Studies: A Guide for Quantitative Researchers Book

	Acknowledgments	vii
Chapter 1	Introduction
1.1	Introduction	1
1.2	What Is a Monte Carlo Study?	2
1.2.1	Simulating the Rolling of a Die Twice	2
1.3	Why Is Monte Carlo Simulation Often Necessary?	4
1.4	What Are Some Typical Situations Where a Monte Carlo Study Is Needed?	5
1.4.1	Assessing the Consequences of Assumption Violations	5
1.4.2	Determining the Sampling Distribution of a Statistic That Has No Theoretical Distribution	6
1.5	Why Use the SAS System for Conducting Monte Carlo Studies?	7
1.6	About the Organization of This Book	8
1.7	References	9
Chapter 2	Basic Procedures for Monte Carlo Simulation
2.1	Introduction	11
2.2	Asking Questions Suitable for a Monte Carlo Study	12
2.3	Designing a Monte Carlo Study	13
2.3.1	Simulating Pearson Correlation Coefficient Distributions	13
2.4	Generating Sample Data	16
2.4.1	Generating Data from a Distribution with Known Characteristics	16
2.4.2	Transforming Data to Desired Shapes	17
2.4.3	Transforming Data to Simulate a Specified Population Inter-variable Relationship Pattern	17
2.5	Implementing the Statistical Technique in Question	17
2.6	Obtaining and Accumulating the Statistic of Interest	18
2.7	Analyzing the Accumulated Statistic of Interest	19
2.8	Drawing Conclusions Based on the MC Study Results	22
2.9	Summary	23
Chapter 3	Generating Univariate Random Numbers in SAS
3.1	Introduction	25
3.2	RANUNI, the Uniform Random Number Generator	26
3.3	Uniformity (the EQUIDST Macro)	27
3.4	Randomness (the CORRTEST Macro)	30
3.5	Generating Random Numbers with Functions versus CALL Routines	34
3.6	Generating Seed Values (the SEEDGEN Macro)	38
3.7	List of All Random Number Generators Available in SAS	39
3.8	Examples for Normal and Lognormal Distributions	45
3.8.1	Random Sample of Population Height (Normal Distribution)	45
3.8.2	Random Sample of Stock Prices (Lognormal Distribution)	46
3.9	The RANTBL Function	51
3.10	Examples Using the RANTBL Function	52
3.10.1	Random Sample of Bonds with Bond Ratings	52
3.10.2	Generating Random Stock Prices Using the RANTBL Function	54
3.10	Summary	57
3.12	References	58
Chapter 4	Generating Data in Monte Carlo Studies
4.1	Introduction	59
4.2	Generating Sample Data for One Variable	60
4.2.1	Generating Sample Data from a Normal Distribution with the Desired Mean and Standard Deviation	60
4.2.2	Generating Data from Non-Normal Distributions	62
4.2.2.1	Using the Generalized Lambda Distribution (GLD) System	62
4.2.2.2	Using Fleishman's Power Transformation Method	66
4.3	Generating Sample Data from a Multivariate Normal Distribution	71
4.4	Generating Sample Data from a Multivariate Non-Normal Distribution	79
4.4.1	Examining the Effect of Data Non-normality on Inter-variable Correlations	80
4.4.2	Deriving Intermediate Correlations	82
4.5	Converting between Correlation and Covariance Matrices	87
4.6	Generating Data That Mirror Your Sample Characteristics	90
4.7	Summary	91
4.8	References	91
Chapter 5	Automating Monte Carlo Simulations
5.1	Introduction	93
5.2	Steps in a Monte Carlo Simulation	94
5.3	The Problem of Matching Birthdays	94
5.4	The Seed Value	98
5.5	Monitoring the Execution of a Simulation	98
5.6	Portability	100
5.7	Automating the Simulation	100
5.8	A Macro Solution to the Problem of Matching Birthdays	101
5.9	Full-Time Monitoring with Macros	103
5.10	Simulation of the Parking Problem (Renyi's Constant)	105
5.11	Summary	116
5.12	References	116
Chapter 6	Conducting Monte Carlo Studies That Involve Univariate Statistical Techniques
6.1	Introduction	117
6.2	Example 1: Assessing the Effect of Unequal Population Variances in a T-Test	118
6.2.1	Computational Aspects of T-Tests	119
6.2.2	Design Considerations	119
6.3.3	Different SAS Programming Approaches	120
6.3.4	T-Test Example: First Approach	121
6.3.5	T-Test Example: Second Approach	125
6.3	Example 2: Assessing the Effect of Data Non-Normality on the Type I Error Rate in ANOVA	129
6.3.1	Design Considerations	130
6.3.2	ANOVA Example Program	130
6.4	Example 3: Comparing Different R[superscript 2] Shrinkage Formulas in Regression Analysis	136
6.4.1	Different Formulas for Correcting Sample R[superscript 2] Bias	136
6.4.2	Design Considerations	137
6.4.3	Regression Analysis Sample Program	138
6.5	Summary	143
6.6	References	143
Chapter 7	Conducting Monte Carlo Studies for Multivariate Techniques
7.1	Introduction	145
7.2	Example 1: A Structural Equation Modeling Example	146
7.2.1	Descriptive Indices for Assessing Model Fit	146
7.2.2	Design Considerations	147
7.2.3	SEM Fit Indices Studied	148
7.2.4	Design of Monte Carlo Simulation	148
7.2.4.1	Deriving the Population Covariance Matrix	150
7.2.4.2	Dealing with Model Misspecification	151
7.2.5	SEM Example Program	152
7.2.6	Some Explanations of Program 7.2	155
7.2.7	Selected Results from Program 7.2	160
7.3	Example 2: Linear Discriminant Analysis and Logistic Regression for Classification	161
7.3.1	Major Issues Involved	161
7.3.2	Design	162
7.3.3	Data Source and Model Fitting	164
7.3.4	Example Program Simulating Classification Error Rates of PDA and LR	165
7.3.5	Some Explanations of Program 7.3	168
7.3.6	Selected Results from Program 7.3	172
7.4	Summary	173
7.5	References	174
Chapter 8	Examples for Monte Carlo Simulation in Finance: Estimating Default Risk and Value-at-Risk
8.1	Introduction	177
8.2	Example 1: Estimation of Default Risk	179
8.3	Example 2: VaR Estimation for Credit Risk	185
8.4	Example 3: VaR Estimation for Portfolio Market Risk	199
8.5	Summary	211
8.6	References	212
Chapter 9	Modeling Time Series Processes with SAS/ETS Software
9.1	Introduction to Time Series Methodology	213
9.1.1	Box and Jenkins ARIMA Models	213
9.1.2	Akaike's State Space Models for Multivariate Times Series	216
9.1.3	Modeling Multiple Regression Data with Serially Correlated Disturbances	216
9.2	Introduction to SAS/ETS Software	216
9.3	Example 1: Generating Univariate Time Series Processes	218
9.4	Example 2: Generating Multivariate Time Series Processes	221
9.5	Example 3: Generating Correlated Variables with Autocorrelated Errors	228
9.6	Example 4: Monte Carlo Study of How Autocorrelation Affects Regression Results	234
9.7	Summary	243
9.8	References	243
	Index	245