Chapter 18 Four Multivariate Techniques

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Chapter 18Four Multivariate Techniques

• Angela Gillis Winston Jackson
• Nursing Research Methods Interpretation

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Multiple Regression

• Multiple regression used when we wish to examine
  the impact of several variables on a dependent
  variable. It is may be used when you have a ratio
  level dependent variable and, preferably, ratio
  level independent variables. There are methods,
  however, for using independents measured at the
  nominal or ordinal levels.

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Multiple Regression Cont.

• Multiple regression is a powerful tool because it
  allows the researcher to
• estimate the relative importance of independent
  variables in predicting variation in a dependent
  variable
• identify an equation describing the relation
  between the independent and dependent variables

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Multiple Regression Cont.

• Elements in the equation tell us the relative
  importance of each factor is in predicting the
  dependent variable.
• Recall from the correlation analysis (Chapter 11)
  the formula Y a bX
• Multiple Regression extends the equation where
• Y a b1X1 b2X2 bkXk

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Y a b1X1 b2X2 bkXk

• a This value represents the constant--the point
  where the regression line crosses the Y axis.
• b These coefficients represent the weightings
  for each of the independent variables.

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Y a ß1X1 ß2X2 ßkXk

• ß These values are knows as beta weights.
• A beta weight simply represents a standardized
  version of a b coefficient.
• Think of ßs as Z-score versions of the b
  coefficients. Recall that Z scores standardize
  variables

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Y a ß1X1 ß2X2 ßkXk

• To compute the relative importance of variables
  once we have the betas we can use the following
  formula
• Variance explained ß1 x R2
• by each variable
  x 100
• 
  ? ßs

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Multiple Regression Cont.

• When you do your SPSS run the program will
  produce both b and ßvalues. The a value (called
  the Constant) will also be printed.
• R2 This value will also be reported which tells
  you how much of the variance in the dependent
  variable is explained by the equation

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Using Non-Ratio Variables

• Ordinal variables may be included in their raw
  form (un-recoded) but remember that the equation
  will underestimate the relative importance of
  non-ratio variables
• Nominal variables may be included by transforming
  them into dummy variables
• Dummy variables are recoded to presence/absence
  variables.

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Dummy Variables

• Create new variables to replace the nominal
  variable so that you have one fewer variables
  than categories in the original variable. I.e.,
  if you have a 3 category religion variable
  (Protestant, Catholic, Jew) then recode this into
  two new variables coded into presence/absence.
  (See p. 566 of text.) Presence 1 Absence 0.

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Tips for Regression Analysis

• Ensure variables are independent of the dependent
  variable, not an alternative measure of it.
• Watch for highly correlated independent variables
  (multicollinearity). Either convert these into an
  index (if that makes sense) or simply select one
  of them.

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Tips Cont.

• Try to achieve ratio level measurement
• Use Raw data do not use recoded forms of ordinal
  or ratio variables
• Use the Backward option when using regression
• Interpret weightings with care.

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Tips Cont.

• Monitor number of cases watch out for cases
  where N is getting close to number of variables.
  (Cases total df 1 on table)
• Repeat analysis eliminating those variables that
  were dropped early in the analysis keep in last
  two or three before final equation
• Try Pairwise solution
• Try Means solution where missing values set to
  mean for the variable

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Discriminant Analysis

• Very similar to Regression analysis but used in
  cases where the researcher has a nominal
  dependent variable.
• Results in the calculation of discriminant
  coefficients similar to a regression equation
• D B0 B1X1 B2X2 ... BkXk

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D B0 B1X1 B2X2 ... BkXk

• B0 This is the constant
• B1 The coefficient for the 1st variable
• To compute the discriminant score multiply the
  coefficient by the observed value (see Table
  18.3, p. 572).

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Discriminant Analysis Cont.

• Discriminant analysis assumes ratio level
  independent variables (similar to regression) but
  like regression dummy variables may be included.
• Both standardized and unstandardized coefficients
  are provided on the output.
• If you want to calculate relative contributions
  use the standardized version

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Discriminant Analysis Cont.

• When discriminant is run you will get a report on
  the of cases which can be correctly classified
  by using the information on the independent
  variables.
• The analysis relies on Lambda. This statistic
  measures the proportionate reduction in error
  that results with knowledge of the independent
  variables.