SlideShare a Scribd company logo
Ingo Bentrott
      School of Marketing
University of Technology, Sydney
   “Vinod Shetty, of Mumbai, secretary of the newly formed
    Young Professionals Collective, said staff were subject to so
    much abuse that thousands of its workers were quitting in
    despair. The problem has become so bad that remaining
    workers are being forced to extend their shifts to 12 to 13
    hours a day to fill the gaps.

Although a call centre worker in India earns about $70 a week-
  twice as much as most professionals in a nation suffering
  chronic underemployment- up to 60 per cent leave their jobs
  each year.”
   (insert graph and logistics regression)

   If you run a logistic regression for BUY using
    the data on the left, you will get a response
    like the graphic on the right

   This is due to the well known issue of
    Listwise Deletion (LD)
   There are two types of non-response: complete non-
    response, where the person does not participate at all in
    the survey and item non-response where a survey is only
    partially completed

   Coleman (1991) mentioned that the rates of non-
    responses have remained constant but Jarvis (2002) says
    the rates are increasing when you control for answering
    machines.

   Respondents have grown to „strongly dislike‟ phone
    surveys.
    ◦ The primary concern is privacy, which has been made worse by
      well-publicized breaches in security (Jarvis 2002)

   In essence, whenever you have missing data in your data,
    you are forced to somehow address it
    ◦ Delete or Impute
   Missing data can be of three types
    ◦ Missing Completely at Random (MCAR)
      Missings are unrelated to the value of x or any other
       variable

    ◦ Missing at Random (MAR)
      Missing not a function of x when „controlled for other
       variable effects.‟

    ◦ Non-ignorable missing
      Missing caused by an unmeasured variable
   Most current discrete choice studies are using stated preference
    designs
    ◦ Creates orthogonal Xs

   This is a way to reduce the number of respondents by getting as
    much data as possible out of fewer respondents

   Discrete choice studies based on Random Utility Theory (RUT) can
    give you excellent estimation of willingness to pay estimates (WTP)
    ◦ Is necessary to have complete cases for low variance estimation

   If data is collected by same survey instrument, it is likely to have the
    same missing pattern across the Xs (Howell, 1998).

   Revealed Preference (RP) data usually has multicollinearity issues
    and the use of missing data indicators will exacerbate this issue.
   (insert graph)

   From our example a bit ago, using most
    multiple imputation techniques would still
    have problems imputing a value for USER
    RATING above.

   If the only variables that can be used are AGE,
    INCOME and POST CODE, missings would be
    a linear combination of these
   Many statistics packages use Listwise Deletion (LD) by default when
    estimating a discrete choice model.
    ◦ In SEM models, VAR-COV matrix only uses valid data for
      estimation

   Leads to selection bias and estimates with reduced efficiency

   If data is MCAR, only penalty is loss of power

   Mean Imputation takes multiple imputes to the same data point and
    averages the results
    ◦ MI is a main-effects only model, CART/MARS use interactions so
      we may not need multiple imputes

   “Hot Deck” imputation (Little and Rubin, 1987) is a technique when
    you use values based on similar cases (similar to surrogates in
    CART)
   Expected Maximization (EM) has been successfully
    applied to missing data but standard errors must be
    obtained using auxiliary methods.
    ◦ Missing imputed during EM

   FIML and ML methods assume multivariate normality
    ◦ These techniques are best when there are a few, distinct
      patterns of missing data (Little, Schnabel, Baumert, 2000).

   If the data is MAR and not MCAR all the above
    techniques will be biased
    ◦ Since MAR implies another „observed‟ explanatory variable
      is affecting the missing, interactions in CART/MARS can
      pick this up.
   Most missing data tends to act in combination (Borgoni
    and Berrington, 2004)

   We should not try to “break” the multivariate nature of the
    data.
    ◦ CART uses surrogates, so even though we impute data one
      variable at a time, the structure will be preserved.

   Most imputation techniques assume multivariate normal.

   Imputation sometimes assumes data is MCAR but if the
    data has high degree of interactions and non-monotonic,
    CART, by its nature will perform better on data that is MAR

   EM algorithm has been proven to be good but implies
    missings only during estimation
    ◦ CART technique can fill the dataset for later analysis.
   If data has high dimensionality and data sparseness, univariate
    nature of CART will be better able to handle this than Multiple
    Imputation using regression.

   Trees are also less prone to outliers and misspecified models

   Although a multiple iteration tree is shown to be better in Monte
    Carlo studies by using multiple draws from CARTs conditional
    distribution (Borgoni and Berrington, 2004), the results are within a
    standard error of the “one shot” variable at a time CART imputation
    technique.
    ◦ One shot has some added variability (like other techniques) but
      standard errors may be underestimated.
    ◦ Extra information gathered from imputation may offset extra
      variability

   If the data is MCAR, using a simple Pearson Chi Square test of
    Observed versus Expected values validates the imputed values.
   (insert table of Descriptive Statistics)

   The diagnostic, binary-valued variable investigated is whether
    the patient shows signs of diabetes according to World Health
    Organization criteria (i.e., if the 2 hour post-load plasma
    glucose was at least 200 mg/dl at any survey examination or
    if found during routine medical care). The population lives
    near Phoenix, Arizona, USA.
   (insert table of Descriptive Statistics)

   This is a dataset with information about renters
    and homeowners. The dataset is a good mixture of
    categorical and continuous variables with a lot of
    missing data.
   This survey is aimed at gathering some
    information about your preferences for athletic
    shoes. More specifically, the product in question
    is an athletic shoe that is to be used primarily for
    playing a sport (or several sports). For example,
    the shoes could be used for playing basketball,
    tennis, running, hiking, and so on.

   Since the questions asked are from a balanced
    stated preference (SP) design, there are only
    missing values in the demographic questions
   (insert table on Descriptive Statistics)
   This presentation looks at 5 different modeling techniques on
    the 3 datasets mentioned previously.

   Model 1. The first model was a simple logistic regression using
    all variables
    ◦ No transformations
    ◦ Listwise deletion was used for missing values

   Model 2. A MARS model was then run with main effects only and
    all model defaults
    ◦ Since the data is binary, this is a Linear Probability Model (LPM)

   Model 3. Mean imputation was used in a logit model

   Model 4. MARS basis functions were then put into logistic
    regression to recover standard errors and eliminate the need for
    weighted least squares in LPM
   Step 1. Sort the variables with missing values from least to
    worst

   Step 2. Starting with the least missing variable, partition
    the data into one data set with that variable‟s missing
    values and one data set with complete cases

   Step 3. Estimate a tree with the least missing variable as a
    target

   Step 4. Score the data set with missing values from the
    results in step 3

   Step 5. Repeat for the next affected variable until all data
    is filled
   (insert graph)

   Regression by logit will yield a different shape
    than a linear probability model

   Some cases will be classified differently using
    the same basis functions from MARS
   (insert table)
   (insert table)
   The data on Shoe buyers is “real” in that it was an
    SP study that was deployed

   The nature of orthogonal design forced trade offs
    and controls for interactions

   The Pima Indian and Home Owner dataset are
    well known and has well defined patterns
    amongst the Xs

   If the buyers are the class of interest, a
    CART/MARS imputation is clearly preferred
   CART and MARS will perform better on mixed data types and
    should be the preferred imputation modeling technique
    ◦ Possible CART MARS  Logit technique to capture all possible non-
      monotonics

   Web based surveys allow us to see when people quit survey

   Can investigate if the person looked at all questions and refused
    some
    ◦ In mail surveys, this is impossible
    ◦ The web will expand our missing data categories as a complete survey,
      means someone that viewed and answered all the questions (Bosnjak and
      Tuten, 2001)

   If survey respondents are paid, this still works best for reducing
    non-response
    ◦ CART can be used with ROC/Lifts charts to see what is optimal amount of
      payment per completed survey
    ◦ Many companies would be willing to pay for this completeness (Coleman,
      1991)
Imputation Techniques For Market Research Datasets With Missing Values

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Imputation Techniques For Market Research Datasets With Missing Values

  • 1. Ingo Bentrott School of Marketing University of Technology, Sydney
  • 2. “Vinod Shetty, of Mumbai, secretary of the newly formed Young Professionals Collective, said staff were subject to so much abuse that thousands of its workers were quitting in despair. The problem has become so bad that remaining workers are being forced to extend their shifts to 12 to 13 hours a day to fill the gaps. Although a call centre worker in India earns about $70 a week- twice as much as most professionals in a nation suffering chronic underemployment- up to 60 per cent leave their jobs each year.”
  • 3. (insert graph and logistics regression)  If you run a logistic regression for BUY using the data on the left, you will get a response like the graphic on the right  This is due to the well known issue of Listwise Deletion (LD)
  • 4. There are two types of non-response: complete non- response, where the person does not participate at all in the survey and item non-response where a survey is only partially completed  Coleman (1991) mentioned that the rates of non- responses have remained constant but Jarvis (2002) says the rates are increasing when you control for answering machines.  Respondents have grown to „strongly dislike‟ phone surveys. ◦ The primary concern is privacy, which has been made worse by well-publicized breaches in security (Jarvis 2002)  In essence, whenever you have missing data in your data, you are forced to somehow address it ◦ Delete or Impute
  • 5. Missing data can be of three types ◦ Missing Completely at Random (MCAR)  Missings are unrelated to the value of x or any other variable ◦ Missing at Random (MAR)  Missing not a function of x when „controlled for other variable effects.‟ ◦ Non-ignorable missing  Missing caused by an unmeasured variable
  • 6. Most current discrete choice studies are using stated preference designs ◦ Creates orthogonal Xs  This is a way to reduce the number of respondents by getting as much data as possible out of fewer respondents  Discrete choice studies based on Random Utility Theory (RUT) can give you excellent estimation of willingness to pay estimates (WTP) ◦ Is necessary to have complete cases for low variance estimation  If data is collected by same survey instrument, it is likely to have the same missing pattern across the Xs (Howell, 1998).  Revealed Preference (RP) data usually has multicollinearity issues and the use of missing data indicators will exacerbate this issue.
  • 7. (insert graph)  From our example a bit ago, using most multiple imputation techniques would still have problems imputing a value for USER RATING above.  If the only variables that can be used are AGE, INCOME and POST CODE, missings would be a linear combination of these
  • 8. Many statistics packages use Listwise Deletion (LD) by default when estimating a discrete choice model. ◦ In SEM models, VAR-COV matrix only uses valid data for estimation  Leads to selection bias and estimates with reduced efficiency  If data is MCAR, only penalty is loss of power  Mean Imputation takes multiple imputes to the same data point and averages the results ◦ MI is a main-effects only model, CART/MARS use interactions so we may not need multiple imputes  “Hot Deck” imputation (Little and Rubin, 1987) is a technique when you use values based on similar cases (similar to surrogates in CART)
  • 9. Expected Maximization (EM) has been successfully applied to missing data but standard errors must be obtained using auxiliary methods. ◦ Missing imputed during EM  FIML and ML methods assume multivariate normality ◦ These techniques are best when there are a few, distinct patterns of missing data (Little, Schnabel, Baumert, 2000).  If the data is MAR and not MCAR all the above techniques will be biased ◦ Since MAR implies another „observed‟ explanatory variable is affecting the missing, interactions in CART/MARS can pick this up.
  • 10. Most missing data tends to act in combination (Borgoni and Berrington, 2004)  We should not try to “break” the multivariate nature of the data. ◦ CART uses surrogates, so even though we impute data one variable at a time, the structure will be preserved.  Most imputation techniques assume multivariate normal.  Imputation sometimes assumes data is MCAR but if the data has high degree of interactions and non-monotonic, CART, by its nature will perform better on data that is MAR  EM algorithm has been proven to be good but implies missings only during estimation ◦ CART technique can fill the dataset for later analysis.
  • 11. If data has high dimensionality and data sparseness, univariate nature of CART will be better able to handle this than Multiple Imputation using regression.  Trees are also less prone to outliers and misspecified models  Although a multiple iteration tree is shown to be better in Monte Carlo studies by using multiple draws from CARTs conditional distribution (Borgoni and Berrington, 2004), the results are within a standard error of the “one shot” variable at a time CART imputation technique. ◦ One shot has some added variability (like other techniques) but standard errors may be underestimated. ◦ Extra information gathered from imputation may offset extra variability  If the data is MCAR, using a simple Pearson Chi Square test of Observed versus Expected values validates the imputed values.
  • 12. (insert table of Descriptive Statistics)  The diagnostic, binary-valued variable investigated is whether the patient shows signs of diabetes according to World Health Organization criteria (i.e., if the 2 hour post-load plasma glucose was at least 200 mg/dl at any survey examination or if found during routine medical care). The population lives near Phoenix, Arizona, USA.
  • 13. (insert table of Descriptive Statistics)  This is a dataset with information about renters and homeowners. The dataset is a good mixture of categorical and continuous variables with a lot of missing data.
  • 14. This survey is aimed at gathering some information about your preferences for athletic shoes. More specifically, the product in question is an athletic shoe that is to be used primarily for playing a sport (or several sports). For example, the shoes could be used for playing basketball, tennis, running, hiking, and so on.  Since the questions asked are from a balanced stated preference (SP) design, there are only missing values in the demographic questions
  • 15. (insert table on Descriptive Statistics)
  • 16. This presentation looks at 5 different modeling techniques on the 3 datasets mentioned previously.  Model 1. The first model was a simple logistic regression using all variables ◦ No transformations ◦ Listwise deletion was used for missing values  Model 2. A MARS model was then run with main effects only and all model defaults ◦ Since the data is binary, this is a Linear Probability Model (LPM)  Model 3. Mean imputation was used in a logit model  Model 4. MARS basis functions were then put into logistic regression to recover standard errors and eliminate the need for weighted least squares in LPM
  • 17. Step 1. Sort the variables with missing values from least to worst  Step 2. Starting with the least missing variable, partition the data into one data set with that variable‟s missing values and one data set with complete cases  Step 3. Estimate a tree with the least missing variable as a target  Step 4. Score the data set with missing values from the results in step 3  Step 5. Repeat for the next affected variable until all data is filled
  • 18. (insert graph)  Regression by logit will yield a different shape than a linear probability model  Some cases will be classified differently using the same basis functions from MARS
  • 19. (insert table)
  • 20. (insert table)
  • 21. The data on Shoe buyers is “real” in that it was an SP study that was deployed  The nature of orthogonal design forced trade offs and controls for interactions  The Pima Indian and Home Owner dataset are well known and has well defined patterns amongst the Xs  If the buyers are the class of interest, a CART/MARS imputation is clearly preferred
  • 22. CART and MARS will perform better on mixed data types and should be the preferred imputation modeling technique ◦ Possible CART MARS  Logit technique to capture all possible non- monotonics  Web based surveys allow us to see when people quit survey  Can investigate if the person looked at all questions and refused some ◦ In mail surveys, this is impossible ◦ The web will expand our missing data categories as a complete survey, means someone that viewed and answered all the questions (Bosnjak and Tuten, 2001)  If survey respondents are paid, this still works best for reducing non-response ◦ CART can be used with ROC/Lifts charts to see what is optimal amount of payment per completed survey ◦ Many companies would be willing to pay for this completeness (Coleman, 1991)