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Chapter 18 Four Multivariate Techniques

Chapter 18 Four Multivariate Techniques. Angela Gillis & Winston Jackson Nursing Research: Methods & Interpretation. Multiple Regression.

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Chapter 18 Four Multivariate Techniques

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  1. Chapter 18Four Multivariate Techniques Angela Gillis & Winston Jackson Nursing Research: Methods & Interpretation

  2. 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.

  3. 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

  4. 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

  5. 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.

  6. 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

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. 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).

  16. 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

  17. 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.

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