Archive for November, 2010

Sending Surveys to Your Customer List? Building a House Panel May Be Better

November 30, 2010

Many times when companies need information quickly, they conduct brief surveys. A single organization may have hundreds of individual accounts with online survey tools like Zoomerang and SurveyMoney, and each of those employees assigned to such an account may send out surveys of his/her own, depending on the needs of his or her department. The respondents for these surveys is most frequently drawn from the customer list, often pulled from an internal database or from the sales force’s contact management software. This can be a bad idea.

Essentially, what is happening here is that there is no designated owner for marketing research – particularly surveys – in these organizations. As a result, everyone takes it upon himself or herself to collect data via a survey. Since many of these departments have no formal training in questionnaire design, sampling theory, or data analysis, they are bound to get biased, useless results. Moreover, not only does the research process degrade, but customers get confused by incorrectly worded questions and overwhelmed by too many surveys in such a short period of time, causing response rates to go down.

In the November 2010 issue of Quirk’s Marketing Research Review, Jeffrey Henning, the founder and vice president of strategy at Vovici, said that companies must first recognize that customer feedback is an asset and then treat it as such. One way to do that would be to build a house panel – a panel developed internally for the organization’s own use.

To do this, there must be a designated panel owner who is responsible for developing the panel. This should fall within the marketing department, and more precisely, the marketing research group. The panel owner must be charged with understanding the survey needs of each stakeholder; the types of information often sought; the customers who are to be recruited to or excluded from the panel; the information to be captured about each panel member; the maintenance of the panel; and the rules governing how often a panelist is to be surveyed, or which panelists get selected for a particular survey. In addition, all surveys should requisitioned by the interested departments to the marketing research group, who can then ensure best practices using the house panel are being followed and that duplication of effort is minimized if not eliminated.

A house panel can take some time to develop. However, house panels are far preferable to dirty, disparate customer lists, as they preserve customers’ willingness to participate in surveys, ensure that surveys are designed to capture the correct information, and make possible that the insights they generate are actionable.

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Happy Thanksgiving from Analysights!

November 22, 2010

In observance of Thanksgiving this week, Analysights will not be posting to Insight Central this week.  We will resume next Monday, November 29.  On behalf of Analysights, we wish you and your family and friends a Happy Thanksgiving, and we in turn thank you for taking time out of your day to read our posts!

Forecast Friday Topic: Structural and Reduced Forms

November 18, 2010

(Thirtieth in a series)

Last week, we discussed the identification problem – a common occurrence in forecasting when consistent estimators of the parameters of the equation or model in which we are interested don’t exist. We also discussed how identifying variables unique to one equation but not to the other is the first step to alleviating the identification problem.

Today, we will briefly discuss the next step in solving the identification problem: structural and reduced forms. Because the math can get a little complicated, we won’t be focusing on it here. Like last week, this week’s – and next week’s – post will be theoretical in nature.

Structural and reduced forms get their origin from matrix algebra and involve systems of equations. Indeed, the equations contained within a system are called structural equations because, together, they are developed to explain the hypothesized structure of a given market. Structural equations are based on economic theory and are used to derive the reduced form equations for two-stage least squares regression.

To derive the reduced form equations, one endogenous variable must be placed on the left side of the equation, while all exogenous variables must be placed on the right. You must have one reduced form equation for each endogenous variable present in the system. So, if your system of equations has five endogenous variables, then you must have five reduced form equations.

The process for reducing the form of the structural equations follows that of solving for a system of linear equations:

  1. Set one equation equal to another;
  2. Subtract the endogenous parameter term (estimate times variable) and error term from each side of equation;
  3. Factor both sides;
  4. Divide to solve for the endogenous variable. This gives you the first reduced form equation.
  5. Find the next reduced form equation by substituting the right side of the first reduced form equation into one of the original structural equations.

Essentially, it’s best to think of endogenous variables as dependent variables and of exogenous variables as independent variables; this way, you get the result of the reduced form having precisely the same format as multiple regression models. Given assumptions about future values of exogenous variables, the reduced form can facilitate computation of conditional forecasts of future values of the endogenous variables.

Forecast Friday Resumes Two Weeks From Today

Forecast Friday will not be published next Thursday, in observance of Thanksgiving.  We here at Analysights are very thankful for readers like you who check in every week, and look forward to your continued visits to Insight Central.  Our Forecast Friday post will resume two weeks from today, December 2, in which we will conclude our discussion of simulataneous equations with a post on Two-Stage Least Squares regression analysis.  We here at Analysights wishes you and your family a Happy Thanksgiving.

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Forecast Friday Topic: The Identification Problem

November 11, 2010

(Twenty-ninth in a series)

When we work with regression analysis, it is assumed that outside factors determine each of the independent variables in the model; these factors are said to be exogenous to the system. This is especially of interest to economists, who have long used econometric models to forecast demand and supply for various goods. The price the market will bear for a good or service, for example, is not determined by a single equation, but by the interaction of the equations for both supply and demand. If price was what we were trying to forecast, then a single equation would do us little good. In fact, since price is part of a multi-equation system, performing regression analysis for just demand without supply or vice-versa will result in biased parameter estimates.

This post begins our three-part “series within a series” on “Simultaneous Equations and Two-Stage Least Squares Regression”. Although this topic sounds intimidating, I will not be covering it in much technical detail. My purpose in discussing it is to make you aware of these concepts, so that you can determine when to look beyond a simple regression analysis.

Hence, we start with the most basic concept of simultaneous equations: the Identification problem. Let’s assume that you are the supply chain manager for a beer company. You need to forecast the price of barley, so your company can budget how much money it needs to spend in order to have enough barley to produce its beer; determine whether the price is on an upward trend, so that it could purchase derivatives to hedge its risk; and determine the final price for its beer.

You have statistics for the price and traded quantity of barley for the last several years. You also remember three concepts from your college economics class:

  1. The price and quantity supplied of a good have a direct relationship – producers supply more as the price goes up and less as the price goes down;
  2. The price and quantity demanded of a good have an inverse relationship – consumers purchase less as the price goes up and vice-versa; and
  3. The market price is determined by the interaction of the supply and demand equations.

Since price and quantity are positively sloped for supply and negatively sloped for demand, with only the two variables of quantity and price, you cannot determine – that is identify – the supply and demand equations using regression analysis; the information is insufficient. However, if you can identify variables that are in one equation and not the other, you will be able to identify the individual relations.

In agriculture, the supply of a crop is greatly affected by weather. If you can obtain information on the amount of rainfall in barley producing regions during the years for which you have data, you might be able to identify the different equations. Moreover, production costs impact supply. So if you can obtain information on the costs of planting and harvesting the barley, that too would help. On the demand side, barley’s quantity can be influenced by changes in tastes. If beer demand goes up, so too will the demand for barley; if farm animal raising increases, farmers may need to purchase more barley for animal fodder; and various health fads may emerge, increasing the demands for barley breads and soups. If you can obtain these kinds of information, you are on your way to identifying the supply and demand curves.

Exogenous and Endogenous Variables

Since rainfall affects the supply of barley, but the barley market does not influence the amount of rainfall, rainfall is said to be an exogenous variable, because its value is determined by factors outside of the equation system. Since the demand for beer helps derive the demand for barley, but not the other way around, beer demand is an exogenous variable.

Because price and quantity of barley are part of a demand and supply system, they are determined by the interaction of the two equations – that is by the equation system – so they are said to be endogenous variables.

Identifying an Equation

If you are trying to identify an equation that is part of a multi-equation system, you must have a minimum of one less variable than you do equations excluded from that equation. Hence, if you have a two-equation system, you must have at least one variable excluded from the model you’re trying to identify, that is included in the other equation; if your system has three equations, you need to have at least two variables excluded from the model you want to identify, and so on.

When you have just enough exogenous variables in one equation that is not in the other equation(s), then your equation is just identified. You can use several econometric techniques to estimate just identified systems, however they are quite rare in practice. When you have no exogenous variables that are unique to one equation in the system, your equations are under identified and cannot be estimated with any econometric techniques. Most often, equations are over identified, because there are more exogenous variables excluded from one equation than required by the number of equations in the system. When over identification is the case, then two-stage least squares (the topic of the third post of this miniseries) is required in order to tell which of the variables is causing your supply (or demand) curve to shift along the fixed demand (or supply) curve.

Next Forecast Friday Topic: Structural and Reduced Forms

Next week’s Forecast Friday topic builds on today’s topic with a discussion of structural and reduced forms of equations. These are the first steps in Two-Stage Least Squares Regression analysis, and are part of the effort to solve the identification problem.

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Be Sure to Follow us on Facebook and Twitter !

Thanks to all of you, Analysights now has nearly 200 fans on Facebook … and we’d love more!  If you like Forecast Friday – or any of our other posts – then we want you to “Like” us on Facebook! And if you like us that much, please also pass these posts on to your friends who like forecasting and invite them to “Like” Analysights! By “Like-ing” us on Facebook, you and they will be informed every time a new blog post has been published, or when new information comes out. Check out our Facebook page! You can also follow us on Twitter. Thanks for your help!

Forecast Friday Topic: The Logistic Regression Model

November 4, 2010

(Twenty-eighth in a series)

Sometimes analysts need to forecast the likelihood of discrete outcomes: the probability that this outcome will occur or that outcome will occur. Last week, we discussed the linear probability model (LPM) as one solution. Essentially, the LPM looked that the two discrete outcomes: a 1 if the outcome occurred and a 0 if it did not. We treated that binary variable as the dependent variable and then ran it as if it were ordinary least squares. In our example, we got a pretty good result. However, LPM came up short in many different ways: values that fell outside the 0 to 1 range, dubious R2 values, heteroscedasticity, and non-normal error terms.

One of the more popular improvements on the LPM is the logistic regression model, sometimes referred to as the “logit” model. Logit models are very useful in consumer choice modeling. While the theory is quite complex, today we will introduce you to basic concepts of the logit model, using a simple regression model.

Probabilities, Odds Ratios, and Logits, Oh My!    

The first thing to understand about logistic regression is the mathematics of the model. There are three calculations that you need to know: the probability, the odds ratio, and the logits. While these are different values, they are three ways of expressing the very same thing: the likelihood of an outcome occurring.

Let’s start with the easiest of the three: probability. Probability is the likelihood that a particular outcome will happen. It is a number between 0 and 1. A probability of .75 means that an outcome has a 75% chance of occurring. In a logit model, the probability of an observation having a “success” outcome (Y=1) is denoted as Pi. Since Pi is a number between 0 and 1, that means the probability of a “failure” outcome (Y=0) is 1- Pi. If Pi (Y=1)=0.40 then Pi (Y=0)=1.00-0.40 = 0.60.

The odds ratio, then, is the ratio of the probability of a success to the probability of failure:

 

Hence, in the above example, the odds ratio is (0.40/0.60) = 0.667.

Logits, denoted as Li, are the natural log of the odds ratio:

Hence the logit in our example here is ln(0.667) = -0.405.

A logistic regression model’s equation generates Ŷ values in the form of logits for each observation. The logits are equal to the terms of a regression equation:

Once an observation’s logit is generated, you must take its antilog to derive its odds ratio, and then you must use simple algebra to compute the probability.

Estimate the Logit Model Using Weighted Least Squares Regression

Because data with a logistic distribution are not linear, linear regression is often not appropriate for modeling; however, if data can be grouped, ordinary least squares regression can be used to estimate the logits. This example will use a simple one-variable model to approximate logits. Multiple logistic regression is beyond the scope of this post, and should only be used with a statistical package.

We use weighted least squares (WLS) techniques for approximating the logits. You will recall that we discussed WLS in our Forecast Friday post on heteroscedasticity. In a logistic distribution, error terms are heteroscedastic, making WLS an appropriate tool to employ. The steps in this process are:

  1. Group the independent variable, each group being its own Xi.
  2. Note the sample size, Ni of each group, and count the number of successes, ni, in each.
  3. Compute the relative probabilities for each Xi:

  1. Use WLS to transform the model with weights, wi:

  2. Perform OLS on the weighted, or transformed model:

     

    L*-hat is computed by multiplying L-hat by the weight, w. Likewise X* is computed by multiplying the original X value by weight; similar for error term.

  3. Take the antilog of the logits to estimate probabilities for each group.

 

Predicting Churn in Wireless Telephony

Marissa Martinelli is director of customer retention for Cheapo Wireless, a low-end cell phone provider. Cheapo’s target market are subprime households, whose incomes are generally below $50,000 per year and don’t have bank accounts. As incomes of their customers rise, churn rates for low-end cell phones increases greatly. Cheapo has developed a new cell phone plan that caters to higher income customers, so that it can migrate its existing customers to the new plan as their incomes rise. In order to promote the new plan, Marissa must first identify the customers most at risk of churning.

Marissa takes a random sample of 1,365 current and former Cheapo cell phone customers and looks at their churn rates. She has their incomes based on their applications and credit checks when they first applied for wireless service. She decides to break them down into 19 groups, with incomes from $0 to $50,000, in $2,500 increments. For simplicity, Marissa divides the income amounts by $10,000, and decides to group them. The lowest income group, 0.50, is all customers whose incomes are $5,000 or less; the next group, 0.75, are those with incomes between $5,000-$7,500, and so on. Marissa notes the number of churned customers (ni) for each income level and the number of customers for each income level (Ni):

# Churned 

Group Size 

Income level ($10Ks) 

ni

Ni

Xi

1 

20 

0.50 

2 

30 

0.75 

3 

30 

1.00 

5 

40 

1.25 

6 

40 

1.50 

8 

50 

1.75 

9 

50 

2.00 

12 

60 

2.25 

17 

80 

2.50 

22 

80 

2.75

35 

100 

3.00 

40 

100 

3.25 

75 

150 

3.50 

70 

125 

3.75 

62 

100 

4.00 

62 

90 

4.25 

64 

90 

4.50 

51 

70 

4.75 

50 

60 

5.00 

 

As the table shows, of the 60 customers whose income is between $47,500 and $50,000, 50 of them have churned. Knowing this information, Marissa can now compute the conditional probabilities of churn (Y=1) for each income group:

# Churned 

Group Size 

Income level ($10Ks) 

Probability of Churn 

Probability of Retention 

ni

Ni

Xi

Pi

1-Pi

1 

20 

0.50 

0.050 

0.950 

2 

30 

0.75 

0.067 

0.933 

3 

30 

1.00 

0.100

0.900 

5 

40 

1.25 

0.125 

0.875 

6 

40 

1.50 

0.150 

0.850 

8 

50 

1.75 

0.160 

0.840 

9 

50 

2.00 

0.180 

0.820 

12 

60 

2.25 

0.200 

0.800 

17 

80 

2.50 

0.213 

0.788 

22 

80 

2.75 

0.275 

0.725 

35 

100 

3.00 

0.350 

0.650 

40 

100 

3.25 

0.400 

0.600 

75 

150 

3.50 

0.500 

0.500 

70 

125 

3.75 

0.560 

0.440 

62 

100 

4.00 

0.620 

0.380 

62 

90 

4.25 

0.689 

0.311 

64 

90 

4.50 

0.711 

0.289 

51 

70 

4.75 

0.729 

0.271 

50 

60 

5.00 

0.833 

0.167 

 

Marissa then goes on to derive the weights for each income level:

     

Logits 

   Weights 

Pi *(1-Pi)

Pi /(1-Pi)

Li

NiPi(1-Pi)

Wi

0.048 

0.053 

-2.944 

0.950 

0.975 

0.062 

0.071 

-2.639 

1.867 

1.366 

0.090 

0.111 

-2.197 

2.700 

1.643 

0.109 

0.143 

-1.946 

4.375 

2.092 

0.128 

0.176 

-1.735 

5.100 

2.258 

0.134 

0.190 

-1.658 

6.720 

2.592 

0.148 

0.220 

-1.516 

7.380 

2.717 

0.160 

0.250 

-1.386 

9.600 

3.098 

0.167 

0.270 

-1.310 

13.388 

3.659 

0.199 

0.379 

-0.969 

15.950 

3.994 

0.228 

0.538 

-0.619 

22.750 

4.770 

0.240 

0.667 

-0.405 

24.000 

4.899 

0.250 

1.000 

0.000 

37.500 

6.124 

0.246 

1.273 

0.241 

30.800 

5.550 

0.236 

1.632 

0.490 

23.560 

4.854 

0.214 

2.214 

0.795

19.289 

4.392 

0.205 

2.462 

0.901 

18.489 

4.300 

0.198 

2.684 

0.987 

13.843 

3.721 

0.139 

5.000 

1.609 

8.333 

2.887 

 

Now, Marissa must transform the logits and the independent variable (Income level) by multiplying them by their respective weights:

Income level ($10Ks)

Logits 

Weights 

Weighted Income 

Weighted Logits 

Xi

Li

Wi

Xi*

Li*

0.50 

-2.944 

0.975 

0.487 

-2.870 

0.75 

-2.639 

1.366 

1.025 

-3.606 

1.00 

-2.197 

1.643 

1.643 

-3.610 

1.25 

-1.946 

2.092 

2.615 

-4.070 

1.50 

-1.735 

2.258 

3.387 

-3.917 

1.75 

-1.658 

2.592 

4.537

-4.299 

2.00 

-1.516 

2.717 

5.433 

-4.119 

2.25 

-1.386 

3.098 

6.971 

-4.295 

2.50 

-1.310 

3.659 

9.147 

-4.793 

2.75 

-0.969 

3.994 

10.983 

-3.872 

3.00 

-0.619 

4.770 

14.309 

-2.953 

3.25 

-0.405 

4.899 

15.922 

-1.986 

3.50 

0.000 

6.124 

21.433 

0.000 

3.75 

0.241 

5.550 

20.812

1.338 

4.00 

0.490 

4.854 

19.415 

2.376 

4.25 

0.795 

4.392 

18.666 

3.491 

4.50 

0.901 

4.300 

19.349 

3.873 

4.75 

0.987 

3.721 

17.673 

3.674 

5.00 

1.609 

2.887 

14.434 

4.646 

Now, Marissa can run OLS on the transformed model, using Weights (wi) and Weighted Income (X*) as independent variables and the Weighted Logits (L*) as the dependent variable.

Marissa derives the following regression equation:

Interpreting the Model

As expected, weighted income has a positive relationship on likelihood of churn. However, her sample is just 19 observations, so Marissa must be very careful about drawing too strong an inference from these results. While R2 is a strong 0.981, it too must not be relied upon. In fact, it is pretty meaningless in a logit model. Also, notice that there is no intercept term in this model. You will recall that when using WLS to correct for heteroscedasticity, the intercept was lost in the transformed model and actually became its slope. It is equivalent to the slope in an unadjusted regression model, since heteroscedasticity doesn’t bias parameter estimates.

Calculating Probabilities

Now Marissa needs to use this model to assess current customers’ likelihood of churning. Let’s say she sees a customer who makes $9,500 a year. That customer would be in the income group, 1.0. What is that customer’s probability of churning? Marissa takes the weight, 1.643 for her wi and the weighted X* (also 1.643), and plugs them into her equation:

= -4.121

To get to the probability, Marissa must take the antilog of these logits, which will give her the odds ratio: 0.016

Now Marissa calculates this customer’s probability of churning:

So, a customer earning $9,500 per year has less than a two percent chance of churning. Had the customer been earning $46,000, he/she would have had a whopping 98.7% chance of churning!

There are equivalents of R2 that are used for logistic regression, but that discussion is beyond the scope of this post. Today’s post was to give you a primer on the theory of logistic regression.

Next Forecast Friday Topic: The Identification Problem

We have just concluded our discussions on qualitative choice models. Next week, we begin our three-part miniseries on Simultaneous Equations and Two-Stage Least Squares Regression. The first post will discuss the Identification problem.

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