*Rein Taagepera*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199534661
- eISBN:
- 9780191715921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534661.003.0004
- Subject:
- Political Science, Comparative Politics, Political Economy

The foremost mental roadblocks in predictive model building are refusal to make outrageous simplifications and reluctance to play with means of extreme cases. “Ignorance-based” models focus on ...
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The foremost mental roadblocks in predictive model building are refusal to make outrageous simplifications and reluctance to play with means of extreme cases. “Ignorance-based” models focus on conceptual constraints: What do we already know about the situation, even before collecting any data? Eliminate the conceptually forbidden areas where data points could not possibly occur, and locate the conceptual anchor points where the value of x imposes a unique value of y. Once this is done, few options may remain for how y can depend on x–unless you tell yourself “It can't be that simple.” A low R 2 may still confirm a predictive model, and a high one may work to reject it.Less

The foremost mental roadblocks in predictive model building are refusal to make outrageous simplifications and reluctance to play with means of extreme cases. “Ignorance-based” models focus on conceptual constraints: What do we already know about the situation, even before collecting any data? Eliminate the conceptually forbidden areas where data points could not possibly occur, and locate the conceptual anchor points where the value of *x* imposes a unique value of *y*. Once this is done, few options may remain for how *y* can depend on *x*–unless you tell yourself “It can't be that simple.” A low *R* ^{2} may still confirm a predictive model, and a high one may work to reject it.

*Rein Taagepera*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199534661
- eISBN:
- 9780191715921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534661.003.0008
- Subject:
- Political Science, Comparative Politics, Political Economy

The outcomes of sociopolitical processes often depend on the factor in shortest supply; this makes multiplication of factors superior to their addition. Naïve linear regression may not detect all ...
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The outcomes of sociopolitical processes often depend on the factor in shortest supply; this makes multiplication of factors superior to their addition. Naïve linear regression may not detect all relationships between physical or social factors, because nonlinear relationships predominate. When x and y can conceptually take only positive values, the simplest conceptually acceptable fit is to connect y to x raised to a power (an exponent). This means that linear regression should be carried out on the logarithms of x and y, not on x and y. Various other constraints, such as forbidden areas and anchor points, lead to exponential, simple logistic, and more complex patterns.Less

The outcomes of sociopolitical processes often depend on the factor in shortest supply; this makes multiplication of factors superior to their addition. Naïve linear regression may not detect all relationships between physical or social factors, because nonlinear relationships predominate. When *x* and *y* can conceptually take only positive values, the simplest conceptually acceptable fit is to connect *y* to *x* raised to a power (an exponent). This means that linear regression should be carried out on the logarithms of *x* and *y*, not on *x* and *y*. Various other constraints, such as forbidden areas and anchor points, lead to exponential, simple logistic, and more complex patterns.

*Rein Taagepera*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199534661
- eISBN:
- 9780191715921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534661.003.0015
- Subject:
- Political Science, Comparative Politics, Political Economy

Take seriously the introductory advice by most introductory texts of statistics: graph the data and look at the graph so as to make sure linear regression makes sense from a statistical viewpoint. ...
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Take seriously the introductory advice by most introductory texts of statistics: graph the data and look at the graph so as to make sure linear regression makes sense from a statistical viewpoint. Graph more than the data – graph the entire conceptually allowed area and anchor points so as to make sure linear regression makes sense from a substantive viewpoint. If using linear regression, report not only the regression coefficients and the intercept but also the ranges, mean values, and medians of all input variables. While symmetric regression has advantages over OLS, fully reported symmetric regression is still merely regression.Less

Take seriously the introductory advice by most introductory texts of statistics: graph the data and look at the graph so as to make sure linear regression makes sense from a statistical viewpoint. Graph more than the data – graph the entire conceptually allowed area and anchor points so as to make sure linear regression makes sense from a substantive viewpoint. If using linear regression, report not only the regression coefficients and the intercept but also the ranges, mean values, and medians of all input variables. While symmetric regression has advantages over OLS, fully reported symmetric regression is still merely regression.

*Richard Evan Schwartz*

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.003.0010
- Subject:
- Mathematics, Educational Mathematics

This chapter contains the statement and proof of the Segment Lemma. It fixes a parameter A = p/q and set P = 2A/(1 + A) and continues the notation from Chapter 8. The chapter is organized as follows. ...
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This chapter contains the statement and proof of the Segment Lemma. It fixes a parameter A = p/q and set P = 2A/(1 + A) and continues the notation from Chapter 8. The chapter is organized as follows. Section 9.2 explains the existence and image of the anchor point. Section 9.3 explains how to reinterpret the classifying map from Section 8.4 as a map defined on a certain subset of R3. The technical result, Lemma 9.4, will be useful for the computations in this chapter. Section 9.4 and 9.5 treats the vertical and horizontal cases of the Segment Lemma, respectively.Less

This chapter contains the statement and proof of the Segment Lemma. It fixes a parameter A = p/q and set P = 2A/(1 + A) and continues the notation from Chapter 8. The chapter is organized as follows. Section 9.2 explains the existence and image of the anchor point. Section 9.3 explains how to reinterpret the classifying map from Section 8.4 as a map defined on a certain subset of **R**^{3}. The technical result, Lemma 9.4, will be useful for the computations in this chapter. Section 9.4 and 9.5 treats the vertical and horizontal cases of the Segment Lemma, respectively.