448:
488:. Theoretical understanding can then guide the modification of the model in such a way as to retain theoretical validity while removing the sources of misspecification. But if it proves impossible to find a theoretically acceptable specification that fits the data, the theoretical model may have to be rejected and replaced with another one.
498:
Another approach to model building is to specify several different models as candidates, and then compare those candidate models to each other. The purpose of the comparison is to determine which candidate model is most appropriate for statistical inference. Common criteria for comparing models
481:
One approach is to start with a model in general form that relies on a theoretical understanding of the data-generating process. Then the model can be fit to the data and checked for the various sources of misspecification, in a task called
306:
and the true underlying value) occurs if an independent variable is correlated with the errors inherent in the underlying process. There are several different possible causes of specification error; some are listed below.
239:
495:
is apposite here: "Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve".
478:
Building a model involves finding a set of relationships to represent the process that is generating the data. This requires avoiding all the sources of misspecification mentioned above.
269:
262:
137:
417:
397:
96:
76:
56:
145:
1016:
355:"Modeling is an art as well as a science and is directed toward finding a good approximating model ... as the basis for statistical inference".
975:
851:
375:
In the example given above relating personal income to schooling and job experience, if the assumptions of the model are correct, then the
792:
432:
282:
has said, "How translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".
891:
788:"Statistical model specification and power: recommendations on the use of test-qualified pooling in analysis of experimental data"
548:
599:
558:
938:
757:
Proceedings of the First US/JAPAN Conference on The
Frontiers of Statistical Modeling: An Informational Approach—Volume 3
755:(1994), "Implications of informational point of view on the development of statistical science", in Bozdogan, H. (ed.),
670:
500:
484:
333:
1021:
609:
519:
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651:
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347:
Note that all models will have some specification error. Indeed, in statistics there is a common aphorism that "
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may affect the independent variables: while this is not a specification error, it can create statistical bias.
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32:
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An irrelevant variable may be included in the model (although this does not create bias, it involves
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568:
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101:
28:
773:(2011). "Misspecification: Wrong regressors, measurement errors and wrong functional forms".
919:
809:
801:
706:; Trivedi, Pravin K. (1993). "Some specification tests for the linear regression model". In
538:
402:
962:; Lahiri, Kajal (2009). "Diagnostic checking, model selection, and specification testing".
382:
770:
752:
715:
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36:
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61:
41:
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poorly represent relevant aspects of the true data-generating process. In particular,
1010:
959:
703:
543:
376:
685:
Model
Selection and Multimodel Inference: A practical information-theoretic approach
506:
492:
326:
234:{\displaystyle \ln y=\ln y_{0}+\rho s+\beta _{1}x+\beta _{2}x^{2}+\varepsilon }
871:
427:. Hence specification diagnostics usually involve testing the first to fourth
20:
987:"A regression error specification test (RESET) for generalized linear models"
906:"Model specification: The views of Fisher and Neyman, and later developments"
924:
905:
838:(2009). "Econometric modeling: Model specification and diagnostic testing".
303:
823:
805:
35:
for the model and choosing which variables to include. For example, given
314:
A variable omitted from the model may have a relationship with both the
951:
666:
290:
Specification error occurs when the functional form or the choice of
936:(1992). "Model specification tests and artificial regressions".
442:
882:(Second ed.). New York: Macmillan Publishers. pp.
459:
318:
and one or more of the independent variables (causing
405:
385:
250:
148:
104:
84:
64:
44:
31:: specification consists of selecting an appropriate
332:The dependent variable may be part of a system of
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An inappropriate functional form could be employed.
16:
Part of the process of building a statistical model
875:
411:
391:
256:
233:
131:
90:
70:
50:
329:and so can lead to poor predictive performance).
731:Objective Knowledge: An evolutionary approach
98:, we might specify a functional relationship
8:
576:, second-order statistical misspecification
351:". In the words of Burnham & Anderson,
923:
813:
404:
384:
368:can help test for specification error in
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209:
193:
171:
147:
103:
83:
63:
43:
683:Burnham, K. P.; Anderson, D. R. (2002),
622:
270:independent and identically distributed
786:Colegrave, N.; Ruxton, G. D. (2017).
667:Quantitative Methods II: Econometrics
27:is part of the process of building a
7:
629:This particular example is known as
648:Principles of Statistical Inference
793:Proceedings of the Royal Society B
712:Testing Structural Equation Models
302:of the difference of an estimated
14:
513:together with its generalization
58:together with years of schooling
549:Data transformation (statistics)
446:
600:Statistical conclusion validity
939:Journal of Economic Literature
863:Regression Modeling Strategies
517:. For more on this topic, see
126:
114:
1:
1017:Regression variable selection
671:College of William & Mary
360:Detection of misspecification
268:that is supposed to comprise
964:Introduction to Econometrics
485:statistical model validation
379:estimates of the parameters
286:Specification error and bias
257:{\displaystyle \varepsilon }
610:Statistical learning theory
520:statistical model selection
336:(giving simultaneity bias).
1038:
761:Kluwer Academic Publishers
652:Cambridge University Press
78:and on-the-job experience
710:; Long, J. Scott (eds.).
564:Exploratory data analysis
878:Elements of Econometrics
631:Mincer earnings function
132:{\displaystyle y=f(s,x)}
861:Harrell, Frank (2001),
735:Oxford University Press
580:Information matrix test
499:include the following:
806:10.1098/rspb.2016.1850
590:Principle of Parsimony
559:Durbin–Wu–Hausman test
413:
412:{\displaystyle \beta }
393:
357:
334:simultaneous equations
258:
235:
133:
92:
72:
52:
985:Sapra, Sunil (2005).
925:10.1214/ss/1177012164
769:Asteriou, Dimitrios;
729:Popper, Karl (1972),
605:Statistical inference
595:Spurious relationship
554:Design of experiments
511:likelihood-ratio test
414:
394:
392:{\displaystyle \rho }
353:
320:omitted-variable bias
292:independent variables
259:
236:
134:
93:
73:
53:
970:. pp. 401–449.
846:. pp. 467–522.
832:Gujarati, Damodar N.
775:Applied Econometrics
585:Model identification
403:
383:
349:all models are wrong
248:
146:
102:
82:
62:
42:
966:(Fourth ed.).
934:MacKinnon, James G.
911:Statistical Science
781:. pp. 172–197.
777:(Second ed.).
534:Abductive reasoning
515:relative likelihood
370:regression analysis
264:is the unexplained
25:model specification
1022:Statistical models
995:Economics Bulletin
842:(Fifth ed.).
840:Basic Econometrics
800:(1851): 20161850.
779:Palgrave Macmillan
718:. pp. 66–110.
708:Bollen, Kenneth A.
574:Heteroscedasticity
458:. You can help by
409:
389:
342:measurement errors
316:dependent variable
273:Gaussian variables
254:
231:
129:
88:
68:
48:
977:978-0-470-01512-4
853:978-0-07-337577-9
844:McGraw-Hill/Irwin
569:Feature selection
491:A quotation from
476:
475:
366:Ramsey RESET test
278:The statistician
91:{\displaystyle x}
71:{\displaystyle s}
51:{\displaystyle y}
29:statistical model
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929:
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897:
881:
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771:Hall, Stephen G.
764:
763:, pp. 27–38
753:Akaike, Hirotugu
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694:
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687:(2nd ed.),
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539:Conceptual model
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836:Porter, Dawn C.
830:
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748:
746:Further reading
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728:
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716:SAGE Publishing
702:
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689:Springer-Verlag
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456:needs expansion
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37:personal income
33:functional form
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960:Maddala, G. S.
956:
946:(1): 102–146.
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918:(2): 160–168.
902:Lehmann, E. L.
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704:Long, J. Scott
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439:Model building
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340:Additionally,
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300:expected value
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893:0-02-365070-2
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544:Data analysis
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467:February 2019
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457:
454:This section
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377:least squares
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280:Sir David Cox
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507:Bayes factor
501:
497:
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483:
480:
477:
464:
460:adding to it
455:
374:
363:
354:
346:
339:
289:
277:
243:
139:as follows:
24:
18:
872:Kmenta, Jan
493:Karl Popper
327:overfitting
1011:Categories
865:, Springer
644:Cox, D. R.
509:, and the
266:error term
21:statistics
1002:(1): 1–6.
433:residuals
421:efficient
407:β
387:ρ
304:parameter
252:ε
229:ε
207:β
191:β
181:ρ
165:
153:
904:(1990).
874:(1986).
824:28330912
646:(2006),
527:See also
425:unbiased
419:will be
952:2727880
884:442–455
815:5378071
431:of the
974:
950:
890:
850:
822:
812:
691:, §1.1
429:moment
244:where
990:(PDF)
968:Wiley
948:JSTOR
617:Notes
298:(the
972:ISBN
888:ISBN
848:ISBN
820:PMID
423:and
399:and
364:The
296:bias
920:doi
810:PMC
802:doi
798:284
669:",
462:.
275:.
19:In
1013::
998:.
992:.
944:30
942:.
914:.
908:.
886:.
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818:.
808:.
796:.
790:.
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714:.
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162:ln
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826:.
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738:.
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