This paper is a critical study on corn (Zea mays) plant with a non linear approach, as it had slow growth rate at the initial stage of the cycle, followed by a rapid growth stage to a critical point then the height growth rate began to decline, reaching to a stability phase. The purpose of this research was to develop such a model to fit the height growth of corn (Zea mays) plant given microbial combination of Ochrobactrum sp.and Bacillus megatirium treatment; besides, to compare the plant absolute growth rate model between plant with microbial and non microbial treatment . A simple sigmoid model was preffered as it is easier to interpret the parameters biologically. The result showed that Logistic model fitted better in describing the height growth compared to Gompertz model, as it yielded coefficient of determination more than 99%. This model showed that the maximum height growth rate happened in about 40 day after planting. Based on the model, it showed that the absolute growth rate tended to be bell-shaped and right-skewed for Logistic and Gompertz, respectively.

The polynomial regression model is extended the multiple linear regression. The selection of Bayesian polynomial regression model with INLA required Criterion. Criterion is using the measure fit model with the available data. There are three criteria, namely DIC, WAIC and CPO. The smaller criterion value from DIC, WAIC and CPO on a model show the best Bayesian polynomial regression model with INLA.

Relationship rice between with height can be described with scatter diagram. Scatter diagram can product the quadratic polynomial regression mod els and the qubic polynomial regression mode which possible. The quadratic polynomial regression model the best variable height and height 2 significant. Then parameter in the quadratic polynomial regression model can be estimated with Bayesian INLA with Gaussian and Empirical Bayes Strategy compare CCD, GRID Strategy. The posterior marginal intercept β0, coefficient β1 and β2 with Gaussian method and different strategy product similar. The posterior marginal of random effects the grid strategy different with CCD and empirical Bayes strategy.