# Analysis of Fluid Velocity inside an Agricultural Sprayer Using Generalized Linear Mixed Models
## 2 Material and Methods
### Useful Sequencing of the Best Model
The results obtained with the best model, through SPSS and SAS, through three iterations, using the information criteria and the estimates of the residual variances (Table 7); using estimated averages for the different levels of FE and theirs p-values (Table 8 and Figure 4); and through the adjustment coefficients of a regression between observed and predicted values, were compared (Table 9). Figure 3: Descriptive statistics of the distribution of fluid velocity according to the variable levels. Histogram of fluid velocity (cm/s) observed inside the sprayer tank according to the liquid level in the tank, pressure, and the number of active nozzles (**a–c**). The curve is theoretical normal. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \(\mathbf{\hat{S}^{2}_{r}}\) & **Standard Error** & **z** & **Lower Limit** & **Upper Limit** \\ \hline
1 & 37.02 & 0.62 & 59.996 & 35.83 & 38.24 \\
2 & 33.00 & 0.55 & 59.987 & 31.94 & 34.09 \\
3 & 36.39 & 0.61 & 59.992 & 35.23 & 37.61 \\
4 & 36.84 & 0.61 & 59.987 & 35.66 & 38.06 \\
5 & 32.38 & 0.54 & 59.983 & 31.34 & 33.45 \\
6 & 32.82 & 0.55 & 59.979 & 31.77 & 33.91 \\
7 & 36.22 & 0.60 & 59.983 & 35.06 & 37.42 \\
8 & 32.20 & 0.54 & 59.975 & 31.17 & 33.27 \\
9 & 28.87 & 0.49 & 59.962 & 27.94 & 29.83 \\
10 & 27.40 & 0.46 & 59.933 & 26.52 & 28.31 \\
11, 12, 13 & 24.76 & 0.41 & 59.845 & 23.96 & 25.58 \\
14 & 30.74 & 0.51 & 59.945 & 29.75 & 31.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of the estimated residual variance (\(\mathbf{\hat{S}^{2}_{r}}\)) of each model, its standard error, the value of the statistic (z), and the values of the lower and upper limits of the 95% confidence interval of the estimated residual variance. The \(p\)-value of the significance test was \(<0.001\) in all models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Structure** & **AICc** & **w\({}_{i}\) (AICc)** & **BIC** & **w\({}_{i}\) (BIC)** & \(\overset{\alpha^{2}}{\sigma}\)_SC_ & \(p\) \\ \hline I & 8371.42 & 0.084 & 8385.18 & 0.353 & 0.056 & \(<\)0.001 \\ \hline AR(1) & 8371.59 & 0.077 & 8392.23 & 0.010 & 0.057 & \(<\)0.001 \\ \hline  & & & & & 0.214 & \(<\)0.001 \\ ARH(1) & 8373.66 & 0.027 & 8414.94 & 0.000 & 0.355 & \(<\)0.001 \\  & & & & & 0.209 & \(<\)0.001 \\  & & & & & 0.159 & 0.001 \\ \hline ARMA(1,1) & 8368.55 & 0.353 & 8396.07 & 0.001 & 0.057 & \(<\)0.001 \\ \hline CS & 8373.33 & 0.032 & 8393.97 & 0.004 & 0.051 & 0.001 \\ \hline  & & & & & 0.051 & \(<\)0.001 \\ CSH & 8376.04 & 0.008 & 8417.31 & 0.000 & 0.138 & \" \\  & & & & & 0.037 & \" \\  & & & & & 0.024 & \" \\ \hline  & & & & & 0.050 & 0.061 \\ D & 8374.09 & 0.022 & 8408.48 & 0.000 & 0.129 & 0.065 \\  & & & & & 0.037 & 0.059 \\  & & & & & 0.023 & 0.087 \\ \hline Toep & 8368.94 & 0.291 & 8403.34 & 0.000 & 0.060 & 0.001 \\ \hline  & & & & & 0.046 & 0.073 \\ UN & 8374.29 & 0.020 & 8449.95 & 0.000 & 0.071 & 0.154 \\  & & & & 0.064 & 0.187 \\  & & & & 0.054 & 0.256 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Adjustment AICc and BIC coefficients and relative weight of each (w\({}_{i}\)). Estimated residual variance (\(\mathbf{\hat{S}^{2}_{r}}\)) was 0.183 in all items, covariance estimation of the random effect –or levels– (\(\beta^{2}\) SC) and p-value as a single value or main diagonal value (random effect levels), according to the covariance matrix structure. _Appl. Sci._**2020**, _10_, 5029