Another AHP Example for Forecasting Goal: Forecasting Next Quarter’s Consumption Pace Criteria: Consumer Confidence; Real Disposable Income; Credit Availability; Interest Rates; Demand for Vehicles; Stock Market Wealth Effect; Katona Effect. Alternatives: Very Strong; Strong; Average; Weak; or Very Weak. How Might This Model Look?

AHP Model for Forecasting Consumer Spending One-Quarter Ahead

How Would You Quantify the Alternatives? Exploratory Data Analysis Techniques Could be Used. One Method: Using a ten-year horizon, determine average growth rate and deviation. From those statistics, determine outcome bounds.

EDA Summary Statistics REAL CONSUMER SPENDING GROWTH (Q/Q, AR) QUARTERLY Data for 42 periods from 1989Q1 to 1999Q2 AVERAGE GROWTH RATE (Geometric Average) = 2.9% Average ABSOLUTE DEVIATION AROUND MEAN = 1.7 pp. NORMAL UPPER BOUND = 3.8% NORMAL LOWER BOUND = 2.1% Maximum value = 6.7%in 1999Q1 Minimum value = -3.1%in 1991Q1 One Approach to Determine Bounds Based on Mean and Deviation Very Strong = Greater than (mean+dev) = Greater than 4.5% Strong= (mean+0.25*dev) to (mean+dev) = 3.4% to 4.5% Moderate= (mean-0.25*dev) to (mean+0.25*dev) = 2.6% to 3.3% Weak= (mean-dev) to (mean-0.25*dev) = 1.2% to 2.5% Very Weak = Less than (mean-dev) = Less Than 1.2%

Example for Real Consumption Growth Very Strong = Greater than or equal to (mean+dev) = Greater than or equal to 4.6% Strong = (mean+0.25*dev) to (mean+dev) = 3.4% to 4.5% Moderate = (mean-0.25*dev) to (mean+0.25*dev) = 2.6% to 3.3% Weak = (mean-dev) to (mean-0.25*dev) = 1.2% to 2.5% Very Weak = Less than (mean-dev) = Less Than 1.2% Or, Use Midpoint Projections VS = ( )/2 = 5.7% S = 4.0% M = 2.9% W = 1.9% VW = ( )/2 = -1.0%

Or, Run Model for High and Low Ranges Scenario 1Scenario 2 Risk of High Growth Risk of Low Growth VS = 6.7% 4.6% S= M= W= VW=

How Would You Quantify the Alternatives (Growth Rates) Using the Saaty 9-Point Relative Comparison Scale? Question: Which Factor Has the Greater Potential Impact on Real Consumer Spending Growth?

Setup Matrix of Pairwise Relative Comparisons CC INCCREDRATECARWLTH KAT Consumer Confidence (CC) 1.0 1/AA 1/BB 1/CC 1/DD 1/EE 1/FF Income (INC) AA 1.0 1/GG 1/HH 1/II 1/JJ 1/KK Credit Availability (CRED) BB GG 1.0 1/LL 1/MM 1/NN 1/OO Interest Rates (inverted impact) (RATE) CC HH LL 1.0 1/PP 1/QQ 1/RR Demand for Vehicles (CAR) DD II MM PP 1.0 1/SS 1/TT Stock Market Wealth Effect (WLTH) EE JJ NN QQ SS 1.0 1/UU Katona Effect (inverted impact) (KAT) FF KK OO RR TT UU 1.0 Saaty Scale =

Setup Matrix of Pairwise Relative Comparisons For Alternatives Saaty Scale = Array the Comparisons This does not have to be the 9-point scale.

Rescaled and Rounded to Nearest Integer. This is one method to understand the process. Saaty, however, would suggest that it is not necessary and may be confusing to add the initial step -- if you do not know how to compare the “very strong” and “weak” implications, for example, he suggests that you set them equal.

Q&A about Pairwise Comparisons VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0 Question: How do you interpret the cells in the matrix? Answer: While it may seem strange to compare, say, the “Very Strong” to the “Weak” criterion, this is precisely what Saaty did in his forecasting application for real growth, which we discussed earlier. But the question that you should ask is, “which outcome is more likely?” Factor Factor Impact on Objective

Q&A about Pairwise Comparisons VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0 Question: How do you interpret the cells in the matrix? Answer: For example, the “factor rating” Very Strong (VS) compared to the “factor rating” of Weak is given a relative weight 1/CC, which alternatively means that the factor rating Weak (W) compared to the factor of Very Strong is the inverse or CC. Factor Factor Impact on Objective

Q&A about Pairwise Comparisons VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0 Question: How do you interpret the cells in the matrix? Answer: So, for example, if you think that the factor intensity is “Strong” (5) for, say income, relative to its impact on consumption and the factor rating for “weak” income is 2, then the cell entry is “5/2”. Do not confuse the rating scale with the magnitude categories in the forecast objective. Factor Factor Impact on Objective

Q&A about Pairwise Comparisons VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0 Question: How do you interpret the cells in the matrix? Answer: Therefore, pairwise-comparison cell (VS,W) or 1/CC is 5/2. Alternatively, the cell (W, VS), which is CC is 2/5, which simply suggests that a very strong gain in income will have a larger impact of strong consumption than a weak income gain. Factor Factor Impact on Objective

Q&A about Pairwise Comparisons VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0 Question: How do you interpret the cells in the matrix? Answer: The numbers in the Saaty scale are independent of the measurement units used. If you enter 2, you mean the larger factor has two times the impact as the smaller factor. Factor Factor Impact on Objective

Q&A about Pairwise Comparisons Question: What if we believe that all choices in the matrix should have the same impact on the objective? Answer: That’s fine and the matrix can be collapsed. VS S M W VW WEIGHT Very Strong (VS) 1.0 1/1 1/1 1/1 1/1= 0.20 Strong (S) /1 1/1 1/1= 0.20 Moderate (M) /1 1/1= 0.20 Weak (W) /1= 0.20 Very Weak (VW) = 0.20 Factor Factor Impact on Objective Example Where the Evaluation of the Factor Intensity is 1 for all comparisons.

Q&A about Pairwise Comparisons Question: What if a factor that typically has a positive impact on the objective will be a negative factor during the horizon of the problem? Answer: That should be reflected in the weights. For example, if income is declining, then you might give it a strong weight for a “weak” reading.

Example for Determining Weights for Declining Income on Consumption

Q&A about Pairwise Comparisons Question: What if you want an absolute scale instead of this relative comparison? Answer: There are various techniques that you can use to develop a quantitative scale. Here is one (known as the Holmes Method): Calculate the correlation (or R 2 is better) between a very strong change in the factor (such as, income) with a very strong change in consumption. Then do the same for a strong change change in the factor with a very strong change in consumption. Use those correlation coefficients to assess the absolute impact. Be careful of timing (leads and lags) relationships.

Q&A about Pairwise Comparisons Answer (Continued): Although this is tedious, EVIEWS can do this easily with a conditional statement. You can also do that in EXCEL, but you must calculate the correlation only using values that meet the condition -- say, real consumption growth greater than 4.5% and real disposable income growth greater than 6.6%(geometric mean plus 1 deviation, ) -- VERY STRONG INCOME GROWTH vs. VERY STRONG CONSUMPTION GROWTH. Similarly that would be done for STRONG INCOME GROWTH (geometric mean plus.25* deviation, which is 4.1%, to 6.5%) vs. VERY STRONG CONSUMPTION GROWTH and so on.

Setup Matrix of Lower Pairwise Comparisons VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0 Question: How Much Impact Does Consumer Confidence Have on Real Consumer Spending Growth? This must be filled in for every alternative...

Finally, collect the individual equations into a spreadsheet.

Determine the Final Forecast Based on Mid-Point Range Estimates (or Some other Criteria). See Next Slide for Additional Breakout Consumer Spending Forecast = 3.0%

Partial Impact of Confidence on Consumer Spending. Consumer Spending IMPACT from CC =.031*CC CC = 0.351*VS+0.173*S+0.106*M+0.150*W+0.220*VW

Limitations of AHP 1. Unicausal Modeling Only. It Does Not Incorporate Feedback Effects. It Assumes the “Criteria” are Relatively Independent over the Time Frame Forecasted. 2. Difficult or Impossible to Check Historical Accuracy.

Some Extensions of AHP Network Modeling with Feedback Analytic Network Process (ANP)

Fast-Food Retail Industry ANP Model

Feedback Network with components having Inner and Outer Dependence among Their Elements C4C4 C1C1 C2C2 C3C3 Feedback Loop in a component indicates inner dependence of the elements in that component with respect to a common property. Arc from component C 4 to C 2 indicates the outer dependence of the elements in C 2 on the elements in C 4 with respect to a common property.

Fast-Food Retail Industry Model Priority Weightings

Burger KingWhite CollarBlue CollarStudentFamilyPriorities White collar1451 / Blue collar1 / 4141 / Student1 / 51 / 411/ Family Pairwise Judgments of the Customer Group for Burger King

Hamburger Model Supermatrix Cluster Priorities Matrix OtherOther Q Ad CompComp OtherQuality CompetitionAdvertising