Hierarchical Linear Regression Analysis: Predicting Dental Health Status, Study Guides, Projects, Research of Marketing

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Hierarchical Linear

Regression Analysis

Alfasoft Online Demo Days Sebastian Ullrich, Diplompsychologe punkt05 Statistikberatung – punkt05.de

• Linear regression analyses are used to predicted a certain quantitative outcome by one or more variables a.k.a. predictors.
• The outcome can be any quantitative variable.
  • A credibility score on a scale from 1 to 100
  • Life expectancy in years
  • Number of sales
• The predictor can be any quantitative or categorical variable.
  • Age in years (quantitative)
  • Marketing budget in EUR (quantitative)
  • Highest education level (categorical, ordinal scale)
  • Country (categorical, nominal scale)

Linear Regression Analysis

• A health insurance company wants to predict the dental health status of their customers to assess future costs.
• An index for dental health is the Community Peridontal Index of Treatment Needs (CPITN).
• Every tooth is rated on a scale from 0 = healthy to 4 = severe periodontitis. The final score in our example is the average score of all teeth.
• Additional variables are age, sex, socioeconomic status (SES), cleaning frequency and the frequency of toothbrush change.
• Which person will have a better or worse dental health status?

Example Data: Dental Health

• Let’s have a look at the costumers age.
• Is there a statistical association between age and CPITN and how are these two variables related?
• To answer both questions we perform a simple linear regression.
  • Outcome / dependent variable: CPITN
  • Predictor / independent variable: age

01: Simple Linear Regression

• Now that we have a regression model (y = b*x + c), we are able to predict a persons outcome using the following equation. - CPITN = 0.033 * age + 1.
• For example, we would predict a CPITN score of 2.62 for a person with the age of 40 and a score of 3.28 for a person with the age of 60. - CPITN = 0.033 * 40 + 1.295 = 2. - CPITN = 0.033 * 60 + 1.295 = 3.
• But how good is our prediction? How close are we to the actual outcome value?

01: Simple Linear Regression Model

• A measure for the goodness of fit is R 2 .
• R 2 provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
• The value of R 2 ranges from 0 to 1.
• 0 = 0%, no variance explained = no prediction
• 1 = 100%, all variance explained = perfect prediction
• In short, the greater the value of R 2 the better the prediction.
• Keep in mind that a value of 1 is somewhat theoretical.
• We wont get a value of 1 in a real life data set. A small proportion of the total variance will always stay unexplained.

Regression model

• By now we only took age into account.
• How does our prediction change when we use age, sex and the socioeconomic status (SES) to predict the CPITN scores?
• Does the cleaning frequency or the frequency of toothbrush change has an effect on the CPITN score?

02: Multiple Linear Regression

• With every predictor we add to our regression model we add another b*x term to the equation. In case of 3 predictors we have the following equation. - y = b 1 *x 1 + b 2 *x 2 + b 3 *x 3 + c - CPITN = 0.038 * age – 0.168 * sex – 0.107 * ses + 1.
• For example, we would now predict a CPITN score of 2.57 for a woman with the age of 40 and middle class ses and a score of 2.74 for a man with the same age and ses. - CPITN = 0.038 * 40 – 0.168 * 2 – 0.107 * 2 + 1.598 = 2. - CPITN = 0.038 * 40 – 0.168 * 1 – 0.107 * 2 + 1.598 = 2.
• But which predictor has the biggest effect on the CPITN score?

02: Multiple Linear Regression Model

• We know by now how we can compare predictors within the same regression model with each other.
• But can we tell whether or not the addition of the cleaning frequency and the frequency of toothbrush change improved our prediction significantly?
• To answer that question, we need to check if there was a statistically significant increase in R 2 . In order to do so we have to compare two regression models. - Model 1: age, sex and socioeconomic status (SES) - Model 2: age, sex, ses, cleaning frequency and the frequency of toothbrush change

03: Hierarchical Linear Regression

• If you are interested in a SPSS course either basic or advanced or even completely customized, feel free to contact Alfasoft or me for more information. - Alfasoft, [email protected] - Sebastian Ullrich, [email protected]
• If you are interested in someone who supports you in your specific data analysis, my colleagues and I are always happy to help. - punkt05 Statistikberatung, [email protected]

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