Find definitions and interpretation for the statistics provided with the Predict analysis.

Use the marginal fitted equations to estimate the population means of the response at different levels of the fixed factors and different values of covariates. The marginal fitted equations assume the means for the random factor terms are zero.

Use the conditional equations to calculate the conditional means for the response at the specific levels of fixed and random factors. Conditional implies conditional on the given levels of the random factors.

Because a mixed effects model include factors, the fitted equations are displayed in a table for all combinations of the factor levels in the model.

Minitab uses the fitted equations and the variable settings to calculate the fits. If the variable settings are unusual compared to the data that was used to estimate the model, a warning is displayed below the prediction.

Use the variable settings table to verify that you performed the analysis as you intended.

The conditional fits are the estimates for the mean response values at both the fixed and the random factor settings given in the data set. The conditional fits are calculated from the conditional fitted equations.

The marginal fits represent mean responses at various fixed factor levels. The marginal fits are calculated from the marginal fitted equations.

The standard error of the fit (SE fit) estimates the variation in the estimated mean response for the specified variable settings. The calculation of the confidence interval for the mean response uses the standard error of the fit. Standard errors are always non-negative.

The degrees of freedom (DF) for the confidence interval (CI) represent the amount of information in the data to estimate the confidence interval for the mean response.

Use the DF to compare how much information is available about different conditional and marginal means. Generally, more degrees of freedom make the confidence interval for the mean narrower than an interval with less degrees of freedom. Because the standard errors for the means are different, the confidence interval for a mean with more degrees of freedom does not have to be narrower than a confidence interval for a mean with fewer degrees of freedom.

These confidence intervals (CI) are ranges of values that are likely to contain the corresponding conditional and marginal mean responses.

Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you sample many times, a certain percentage of the resulting confidence intervals contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

The confidence interval is composed of the following two parts:

- Point estimate
- The point estimate is the estimate of the parameter that is calculated from the sample data. The confidence interval is centered around this value.
- Margin of error
- The margin of error defines the width of the confidence interval and is determined by the observed variability in the sample, the sample size, and the confidence level. To calculate the upper limit of the confidence interval, the error margin is added to the point estimate. To calculate the lower limit of the confidence interval, the error margin is subtracted from the point estimate.

Use the confidence intervals to evaluate whether the conditional and marginal mean responses are statistically larger than, equal to, or less than a specific value. You can also use the confidence intervals to determine a range of values for the corresponding unknown conditional and marginal mean responses.

The degrees of freedom (DF) for the prediction interval (PI) represent the amount of information in the data to estimate the corresponding prediction interval.

The prediction interval is a range that is likely to contain a single future response for a selected combination of variable settings. If you collect another data point at the same variable setting, the new data point is likely to be within the prediction interval. Narrower prediction intervals indicate a more precise prediction.

Use the prediction intervals to assess the precision of the predictions. The prediction intervals help you assess the practical significance of your results. If a prediction interval extends outside of acceptable boundaries, the predictions might not be sufficiently precise for your requirements.

Use the marginal prediction interval when you don't know the actual levels of the random factors. Use the conditional prediction interval when you know the specific combination of the random factor settings.

In these results, the prediction intervals indicate that you can be 95% confident that a single new yield for variety 1 of alfalfa from field 1 will be between 3.462 and 4.309, and a single new yield for variety 1 of alfalfa from a randomly selected field will be between 2.536 and 4.424.

Mixed Effects Model Information
Terms
Field Variety

Settings
Variable Setting
Field 1
Variety 1

Prediction
Type Fit SE Fit CI DF 95% CI PI DF 95% PI
Conditional 3.885 0.103 15.58 (3.666, 4.104) 15.16 (3.462, 4.309)
Marginal 3.480 0.163 4.92 (3.058, 3.902) 4.92 (2.536, 4.424) X
X denotes an unusual point relative to predictor levels used to fit the model.