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Applied and Environmental Microbiology, May 2001, p. 2129-2135, Vol. 67, No. 5
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.
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
and
*
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.
Present address: National Food Processors Association, Washington,
DC 20005.
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