Using and interpreting restricted cubic splines - Maarten Buis

1 IntroductionSplinesInterpreting the resultsUsing and interpreting restricted cubic splinesMaarten L. BuisInstitut f r SoziologieEberhard Karls Universit t T L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsOutlineIntroductionSplinesInterpr eting the resultsMaarten L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

2 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

3 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

4 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

5 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

6 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

7 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

8 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsThe default is linearIA large part of daily statistical practice consists ofestimating the relationship between two or more default is often to assume the relationships are assumption is (almost) always wrongbut is still a verygood thing:IThe aim of a model is to simplify the situation such thatmere mortals can understand the patterns present in that a relationship is linear is a very natural anduseful talk deals with the rare situation where we want toconsider non-linear could for example occur because.

9 Ithe relationship is too non-linear to be meaningfullysummarized by a linear relationship, orIwe are substantively interested in the L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsOutlineIntroductionSplinesInterpr eting the resultsMaarten L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsA linear association05101510203040 Mileage (mpg)price in 1000 dollarsFitted valuesMaarten L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsHow did I do that?. sysuse auto, clear(1978 Automobile Data). replace price = price / 1000price was int now float(74 real changes made).

10 Label variable price "price in 1000 dollars".. reg price mpgSourceSS df MS Number of obs = 74F( 1, 72) = 1 Prob > F = 72 R-squared = R-squared = 73 Root MSE = Std. Err. t P>|t| [95% Conf. Interval] .0530767 predict y_lin(option xb assumed; fitted values). twoway scatter price mpg || ///> line y_lin mpg, ///> sort clstyle(solid) Maarten L. BuisUsing and interpreting restricted cubic splinesIntroductionSplinesInterpreting the resultsA linear spline05101510203040 Mileage (mpg)price in 1000 dollarsFitted valuesMaarten L.