Summary MVDA - Lecture Notes

Multivariate Data Analysis
Lecture 1
 Relationship between several variables (three or moremultivariate)
 One dependent variable; several independent variables (predictors)
 Which technique is used depends on measurement level of variables (nominal, interval,
binary)
 #




 Residual=difference bw predicted and actual score
 Best prediction is if sum of squared differences is minimal (residuals are minimalnot much
error)
 Constant=where line crosses y-axis
 With two predictors=regression line becomes regression plane
 Use regression model to predict someone’s score
 Evaluating the model:
 Hypothesis testing  if we reject H0, we know that at least one regression coefficient has a
predictive value
 R squared = how good model reflects observed data
 Through standardizing the regression equation, measurement units do not matter
 Semipartial corr (squared part correlations in SPSS) reflects how much var uniquely
explained by one variable
o 3.4% explained by both predictors
o r2 = 0.500 = 50%


50-28.3-18.3=3.4




 Regression Assumptions

, o Interval measurement level
o Dep variable is linear combination of predictors
o Homoscedasticity of residuals (constant across values of predictors)
o Independence of residuals
o Normality of residuals
o No multicollinearity in predictors (inter-correlations)
 Checking assumptions in SPSS


Residual Plot: normal distr. of residuals!




 Check Outliers
 Different types of outliers


k=number of predictors




 What if assumptions are violated?
o Easy fixes:
 Remove predictors that cause violation (often not possible)
 Try transforming the variables (not always works)
o Better:
 Use a more robust regression technique




 Multicollinearity
o Moderate to high inter-corr among predictors
 Limits size of r2
 How important is predictor?
 Unstable regression equation
o Identifying Multicoll.:

Tolerance needs to be above 0.10
VIF needs to be below 10