Abstract
In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 239-247 |
| Number of pages | 9 |
| Journal | Journal of Modern Applied Statistical Methods |
| Volume | 6 |
| Issue number | 1 |
| State | Published - May 2007 |
| Externally published | Yes |
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Keywords
- B-splines
- Likelihood ratio test
- Loglinear model
- Penalized likelihood
- Poisson regression model
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Statistics and Probability
Cite this
A spline-based lack-of-fit test for independent variable effect in poisson regression. / Li, Chin-Shang; Tu, Wanzhu.
In: Journal of Modern Applied Statistical Methods, Vol. 6, No. 1, 05.2007, p. 239-247.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A spline-based lack-of-fit test for independent variable effect in poisson regression
AU - Li, Chin-Shang
AU - Tu, Wanzhu
PY - 2007/5
Y1 - 2007/5
N2 - In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given.
AB - In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given.
KW - B-splines
KW - Likelihood ratio test
KW - Loglinear model
KW - Penalized likelihood
KW - Poisson regression model
UR - http://www.scopus.com/inward/record.url?scp=48249115994&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=48249115994&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:48249115994
VL - 6
SP - 239
EP - 247
JO - Journal of Modern Applied Statistical Methods
JF - Journal of Modern Applied Statistical Methods
SN - 1538-9472
IS - 1
ER -