lec3 - III.ModelBuilding Modelbuilding:writingamodelthatwill

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    III. Model Building
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    Model building:  writing a model that will  provide a good fit to a set of data & that will  give good estimates of the mean value of  y   and good predictions of  y  for given values  of the explanatory variables.
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      Why is model building important, both in  statistical analysis & in analysis in general?  Theory & empirical research
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     “A social science theory is a reasoned and precise  speculation about the answer to a research  question, including a statement about why the  proposed answer is correct.”  “Theories usually imply several more specific  descriptive or causal hypotheses” (King et al., page  19).
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     A model is “a simplification of, and  approximation to, some aspect of the world.”  “Models are never literally ‘true’ or ‘false,’  although good models abstract only the ‘right’  features of the reality they represent” (King et  al., page 49).
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     Remember: social construction of reality  (including alleged causal relations);  skepticism; rival hypotheses; &  contradictory evidence.  What kinds of evidence (or perspectives)  would force me to revise or jettison the  model?
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    Three approaches to model building   Begin with a linear model for its simplicity & as  a rough approximation of the y/x relationships.  Begin with a curvilinear model to capture the  complexities of the y/x relationships.  Begin with a model that incorporates linearity  &/or curvilinearity in y/x relationships according  to theory & observation.
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      The predominate approach used to be to start with a  simple model & to test it against progressively more  complex models.  This approach suffers, however, from the problem  associated with omitted variables in the simpler models.   Increasingly common, then, is the approach of  starting with more complex models & testing against  simpler models  (Greene,  Econometric Analysis , pages  151-52).
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     The point of departure for model-building is  trying to grasp  how the outcome variable  y   varies as the levels of an explanatory variable  change .   We have to know  how to write a mathematical  equation to model this relationship .
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     In what follows, let’s pretend that we’ve already  done careful univariate & bivariate exploratory data  analysis via graphs & numerical summaries  (although, on the other hand, the exercise requires  here & there that we didn’t do such careful  groundwork…).
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     Suppose we want to model a person’s  performance on an exam,  y , as a function of a  single explanatory variable,  x
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lec3 - III.ModelBuilding Modelbuilding:writingamodelthatwill

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