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Comparison of time to the event and nonlinear regression models in the analysis of germination data
Majid Azimmohseni, Farshid Ghaderi-Far, Mahnaz Khalafi, Hamid Reza Sadeghipour, Marzieh Ghezel,
Volume 9, Issue 1 ((Spring and Summer) 2022)
Abstract

Extended abstract
  Introduction: Numerous studies are being carried out to reveal the effects of different treatments on the germination of seeds from various plants. The most commonly used method of analysis is the nonlinear regression which estimates germination parameters. Although the nonlinear regression has been performed based on different models, some serious problems in its structure and results motivated researchers to investigate alternative approaches with higher accuracy and precision. The main purpose of the present research is to introduce the alternative parametric time to event model and comparing its reliability to the nonlinear regression in experiments carried out under different conditions.
  Materials and Methods:  The results of four different experiments were used here including the effect of Potassium cyanide on walnut seed germination, the effect of salinity on wheat seed germination, the effect of water potential on corn seed germination and the effect of temperature on cotton seed germination. The nonlinear regression and time to event methods were applied based on the Gompertz model. The obtained standard errors from the two models were further assessed using the Monte-Carlo method.
  Results: Both methods provided well-fitting models according to the MSE and R2   criteria. Although the germination parameters were approximately identical in both models, the standard error of parameters in nonlinear regression was significantly less than those of time to event method except for the experiments in which all tested seeds germinated within the time frame of study so that in the latter case the estimated standard errors in both models were identical. The Monte-Carlo method confirmed the results of the time to event model and reveals the underestimation of the nonlinear regression method in estimating the standard error of parameters.
  Conclusions: Generally, the results of this research showed that the time to event model can be trustfully utilized in seed germination studies under different conditions and treatments. This model, not only provides precise estimates of the germination parameters but also provides the precise standard error of parameters that have important roles in making inferences for parameters. The drc package in R software enables researchers to fit the different time to event models.

 
Highlights:
  1. Using the time to the event model in estimation of seed germination parameters.
  2. Comparing the time to event and nonlinear regression methods in different seed germination experiments.
  3. Using the Monte-Carlo method for investigating the accuracy of results of the used methods.
 
 
 
 
 
 
Evaluation of the generalized linear model to the germination percentage data and its comparison with the square root transformation
Farshid Ghaderi-Far, Majid Azimmohseni, Seyed Hamidreza Bagheri,
Volume 10, Issue 2 ((Autumn & Winter) 2024)
Abstract
Extended abstract
Introduction: In seed research, germination percentage data is the result of counting and has a binomial distribution. Therefore, seed researchers use data transformation, especially square root transformation, to stabilize the variance and normalize the data before performing analysis of variance and comparison of treatments. Despite the use of data transformation, this method has fundamental issues in the structure that misleads the test results. Therefore, it is important to introduce and replace a method that preserves the research assumptions and provides acceptable results for researchers without using data transformation. The use of generalized linear model is an alternative method for analyzing germination data with binomial distribution. In this research, the generalized linear model will be introduced first. Then, the efficiency of this method will be illustrated using simulated and actual germination data.
Materials and Methods: In this research, first the simulated data was generated by the Monte Carlo method. Based on the simulated data, the significance level and the power of test of generalized linear model were computed. Then the actual data related to three experiments including the effect of acidity on germination of wheat varieties, the effect of water stress and salinity on germination of yellow sweet clover seeds, and the effect of alternating temperatures on germination of three lavender populations were used and the results of the generalized linear model were compared with the square root transformation method based on the data of three experiments.
Results: The simulation results showed that the generalized linear model has a high efficiency to preserve the predetermined significance level and a high power in detecting significant differences in germination of the treatments. Moreover, the results of the comparison of the generalized linear model with the square root transformation method illustrated that the generalized linear model had a higher capability to detect significant differences between various treatments, especially in the treatments with unequal seeds in the Petri dish, and in the treatments in which the square root transformation method resulted in no significant difference among treatments, the generalized linear method showed a significant difference.
Conclusions: Generally, the results of this research demonstrated that the generalized linear model can be used as an alternative method to square root transformation in studies on the germination percentage of seeds with binomial distribution, without having the problems of the square root transformation method. Moreover, this model outperforms the square root transformation in detecting significant differences in germination of treatments with fixed and different seeds.

Highlights:
  1. The generalized linear model was used for the analysis of germination percentage data.
  2. The data simulated using the Monte-Carlo method was utilized to examine the significance level and power of the generalized linear model test.
  3. The generalized linear model was compared with the square root transformation method during different germination experiments with fixed and different seeds in each Petri dish.

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