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Applied and Environmental Microbiology, May 2001, p. 2129-2135, Vol. 67, No. 5
0099-2240/01/$04.00+0   DOI: 10.1128/AEM.67.5.2129-2135.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.

Comparison of Logistic Regression and Linear Regression in Modeling Percentage Data

Lihui Zhao, Yuhuan Chen,dagger and Donald W. Schaffner*

Department of Food Science, Cook College, the New Jersey Agricultural Experiment Station, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08901-8520

Received 3 November 2000/Accepted 27 February 2001

Percentage is widely used to describe different results in food microbiology, e.g., probability of microbial growth, percent inactivated, and percent of positive samples. Four sets of percentage data, percent-growth-positive, germination extent, probability for one cell to grow, and maximum fraction of positive tubes, were obtained from our own experiments and the literature. These data were modeled using linear and logistic regression. Five methods were used to compare the goodness of fit of the two models: percentage of predictions closer to observations, range of the differences (predicted value minus observed value), deviation of the model, linear regression between the observed and predicted values, and bias and accuracy factors. Logistic regression was a better predictor of at least 78% of the observations in all four data sets. In all cases, the deviation of logistic models was much smaller. The linear correlation between observations and logistic predictions was always stronger. Validation (accomplished using part of one data set) also demonstrated that the logistic model was more accurate in predicting new data points. Bias and accuracy factors were found to be less informative when evaluating models developed for percentage data, since neither of these indices can compare predictions at zero. Model simplification for the logistic model was demonstrated with one data set. The simplified model was as powerful in making predictions as the full linear model, and it also gave clearer insight in determining the key experimental factors.


* Corresponding author. Mailing address: Department of Food Science, Cook College, the New Jersey Agricultural Experiment Station, Rutgers, The State University of New Jersey, 65 Dudley Rd., New Brunswick, NJ 08901-8520. Phone: (732) 932-9611, ext. 214. Fax: (732) 932-6776. E-mail: schaffner{at}aesop.rutgers.edu.

dagger Present address: National Food Processors Association, Washington, DC 20005.


Applied and Environmental Microbiology, May 2001, p. 2129-2135, Vol. 67, No. 5
0099-2240/01/$04.00+0   DOI: 10.1128/AEM.67.5.2129-2135.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.



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