Introduction of
Thomas H. Taylor, Jr., PE
 Georgia Institute of Technology, BS Applied Mathematics, 1975
 Georgia State University, MS Decision Sciences, Statistics
Concentration, 1985
 Registered Professional Engineer, Industrial
 25 years in private-sector energy industry + 8 years in micro-biology
and public health, in federal government
 Senior Executive in utility consulting industry
 Senior federal employee, well published in scientific journals.
 Holder of Methods Patent for new computational approach and associated
SASTM-based software for series-dilution bioassays
 Career conclusions:
 Modeling (and much of statistics in general) is transferable across sectors,
industries, and disciplines.
 The jargon varies across sectors, industries, and disciplines
Presentation Outline
 Introduction of T. Taylor
 Regression Modeling Motivation
 Implicit in the development of a real-world model is the expectation that it
be used for decision making.
 The decision-making is the guiding principle for model development.
 Modeling Examples
 Course of Disease – response decisions
 Epidemiological, Chronic – policy and treatment decisions
 Epidemiological, Outbreak – announcements & recalls
 Software for modeling – SASTM is superior to ExcelTM in modeling
situations, due to documentation, reproducibility, and audit-worthiness.
 Regression modeling in the real world is not as clean as it is in many
textbooks
Decision-making and Risk
 Implicit in decision making is the minimization of risk




Risk = probability (event) X loss function (event)
Loss functions are different in different industries and sectors
“Risk” is used incorrectly in some sectors and industries.
Government decision criteria are considerably different from private sector
 Public welfare is not expected to be cost-effective
 Epidemiology
 Objective: Reduce burden of disease or rate of mortality
 Intervention: Vaccine introduction; educational campaigns, e.g. hand-washing;
avoidance of specific behaviors; food and drug recalls
 Energy
 Objective: reduce energy use, or re-arrange energy use
 Actions: green marketing; efficiency mandates; development of alternatives
 Classic Marketing
 Objective: increase sales; maximize profit; minimize risk
 Decisions: pricing, product/service choice; R&D
not
sick
sick
Individual
Spore
eqiuvalent of
tolerance toxin level
Decision/Outcome Criterion
exposure
spores
Exposure=Personal Tolerance
Fulminant
Stage
Prodroma
l
Stage
Exposure >> Personal Tolerance
Fulminant
Stage
Decision Timepoints (from
Model!)
Individual tolerance
100,000
Not sick
50,000
600
3 hrs.
600
50,000
exposure
100,000
Popular Regression Models
Time series
Simple Trends, e.g. energy increase per year
Application-specific functions, e.g. sigmoidal
ARIMA et al
“Causal” – not really: association ≠ cause
Energy
End-use: BTU=f(appliance stock, efficiency)
Econometric: BTU=f(cost of energy, income, inflation)
Epidemiological
Case-status=f(age, sex, race, genetic factors)
Case-status=f(exposure1, exposure2,…)
“Survival” (Time-to-Event) models
SASTM Regression Procedures
General Regression: The REG Procedure
Nonlinear Regression: The NLIN Procedure
Response Surface Regression: The RSREG Procedure
Partial Least Squares Regression: The PLS Procedure
Regression for Ill-conditioned Data: The ORTHOREG Procedure
Local Regression: The LOESS Procedure
Robust Regression: The ROBUSTREG Procedure
Logistic Regression: The LOGISTIC Procedure
Regression with Transformations: The TRANSREG Procedure
Regression Using the GLM, CATMOD, LOGISTIC, PROBIT, and
LIFEREG Procedures
Interactive Features in the CATMOD, GLM, and REG Procedures
http://support.sas.com/onlinedoc/913/docMainpage.jsp
SASTM Regression Help (1)
CATMOD
–
analyzes data that can be represented by a contingency table. PROC CATMOD fits linear models to
functions of response frequencies, and it can be used for linear and logistic regression. The CATMOD
procedure is discussed in detail in Chapter 5, "Introduction to Categorical Data Analysis Procedures."
GENMOD
–
fits generalized linear models. PROC GENMOD is especially suited for responses with discrete outcomes,
and it performs logistic regression and Poisson regression as well as fitting Generalized Estimating
Equations for repeated measures data. See Chapter 5, "Introduction to Categorical Data Analysis
Procedures," and Chapter 29, "The GENMOD Procedure," for more information.
GLM
–
uses the method of least squares to fit general linear models. In addition to many other analyses, PROC
GLM can perform simple, multiple, polynomial, and weighted regression. PROC GLM has many of the same
input/output capabilities as PROC REG, but it does not provide as many diagnostic tools or allow interactive
changes in the model or data. See Chapter 4, "Introduction to Analysis-of-Variance Procedures," for a more
detailed overview of the GLM procedure.
LIFEREG
–
fits parametric models to failure-time data that may be right censored. These types of models are commonly
used in survival analysis. See Chapter 10, "Introduction to Survival Analysis Procedures," for a more detailed
overview of the LIFEREG procedure.
http://v8doc.sas.com/sashtml/
SASTM Regression Help (2)
LOGISTIC
– fits logistic models for binomial and ordinal outcomes. PROC LOGISTIC provides
a wide variety of model-building methods and computes numerous regression
diagnostics. See Chapter 5, "Introduction to Categorical Data Analysis
Procedures," for a brief comparison of PROC LOGISTIC with other procedures.
NLIN
– builds nonlinear regression models. Several different iterative methods are
available.
ORTHOREG
– performs regression using the Gentleman-Givens computational method. For illconditioned data, PROC ORTHOREG can produce more accurate parameter
estimates than other procedures such as PROC GLM and PROC REG.
PLS
– performs partial least squares regression, principal components regression, and
reduced rank regression, with cross validation for the number of components.
http://v8doc.sas.com/sashtml/
SASTM Regression Help (3)
PROBIT
–
performs probit regression as well as logistic regression and ordinal logistic regression. The
PROBIT procedure is useful when the dependent variable is either dichotomous or
polychotomous and the independent variables are continuous.
REG
–
performs linear regression with many diagnostic capabilities, selects models using one of
nine methods, produces scatter plots of raw data and statistics, highlights scatter plots to
identify particular observations, and allows interactive changes in both the regression model
and the data used to fit the model.
RSREG
–
builds quadratic response-surface regression models. PROC RSREG analyzes the fitted
response surface to determine the factor levels of optimum response and performs a ridge
analysis to search for the region of optimum response.
TRANSREG
–
fits univariate and multivariate linear models, optionally with spline and other nonlinear
transformations. Models include ordinary regression and ANOVA, multiple and multivariate
regression, metric and nonmetric conjoint analysis, metric and nonmetric vector and ideal
point preference mapping, redundancy analysis, canonical correlation, and response surface
regression.
http://v8doc.sas.com/sashtml/
SASTM Regression Help (4)
Several SAS/ETS procedures also perform regression. The following procedures are
documented in the SAS/ETS User's Guide.
AUTOREG
–
implements regression models using time-series data where the errors are autocorrelated.
PDLREG
–
performs regression analysis with polynomial distributed lags.
SYSLIN
–
handles linear simultaneous systems of equations, such as econometric models.
MODEL
–
handles nonlinear simultaneous systems of equations, such as econometric models.
http://v8doc.sas.com/sashtml/
Point-and-click vs. SASTM code
SASTM has tremendously more capability
Use of SASTM procedures provides
documentation, formally and operationally
Spreadsheets and point-and-click environments
cannot withstand audits
Regulatory agencies: FERC, FDA, NRC, USDA
(FDA: 21 CFR Part 11)
Labor intensive point-and-click can be replaced
with SASTM code to save time and, therefore,
focus on analysis, not mechanics.
Specific Models
 Disease A (used as decision/outcome example above)
 Course of disease - NOT regression
 Disease P
 Time series
 Simple periodic with exception!
Seasonal Data with
Aberrations
1996
1997
1998
1999
Sinusoidal Piecewise Regression
with Trend
Specific Models
 Disease A
 Course of disease - NOT regression
 Disease P
 Time series
 Simple periodic with exception!
 Sigmoid
 Laboratory applications
Measured
Response
Plot of Measured Response* by Dilution
“Well-behaved” Specimen
*Measured response can be cell counts,
optical density, luminescence, or other labmeasured quantity.
100%
y  B
True Midpoint
(LD50, ED50, etc)
A B
x
1  
C 
0%
Observed
50% Titer
True 50%
Titer
Dilution
D
Observed
Response
What about?… High-Variance Specimens
Robustness of True 50% Endpoint
y  B
A B
x
1  
C 
Midpoint
(50%)
50%
Dilution
D
Specific Models
 Disease A
 Course of disease - NOT regression
 Disease P
 Time series
 Simple periodic with exception!
 Sigmoid
 Laboratory applications
 Investigation of foodborne disease outbreak
 Not a laboratory
 Not a controlled experiment
 Not even a designed experiment
 Observational data
Foodborne Disease Outbreak
Associative (not causal) models
Epidemiological
Case-status=f(exposure1, exposure2,…)
100
Tomatoes
No tomatoes
50
0
Sick People
Not Sick
George Box: “…all models are
wrong, but some are useful.”
 George Edward Pelham Box (18 October 1919 – ) is one of the most
influential statisticians of the 20th century and a pioneer in the areas of
quality control, time series analysis, design of experiments and
Bayesian inference.
 He served as President of the American Statistical Association in 1978
and of the Institute of Mathematical Statistics in 1979. He received the
Shewhart Medal from the American Society for Quality Control in
1968, the Wilks Memorial Award from the American Statistical
Association in 1972, the R. A. Fisher Lectureship in 1974, and the Guy
Medal in Gold from the Royal Statistical Society in 1993. He was
elected a member of the American Academy of Arts and Sciences in
1974 and a Fellow of the Royal Society in 1979.