Use a Pareto chart of the standardized effects to compare the relative magnitude and the statistical significance of both main and interaction effects.
Minitab plots the standardized effects in the decreasing order of their absolute values. The reference line on the chart indicates which effects are significant. By default, Minitab uses a significance level of 0.05 to draw the reference line.
Term | Effect | Coef | SE Coef | VIF |
---|---|---|---|---|
Constant | -2.7370 | 0.0479 | ||
Preservative | 0.4497 | 0.2249 | 0.0477 | 1.03 |
VacuumPress | 0.2574 | 0.1287 | 0.0477 | 1.06 |
ContaminationLevel | 0.2954 | 0.1477 | 0.0478 | 1.06 |
CoolTemp | -0.1107 | -0.0554 | 0.0478 | 1.07 |
Preservative*VacuumPress | -0.0233 | -0.0117 | 0.0473 | 1.05 |
Preservative*ContaminationLevel | 0.0722 | 0.0361 | 0.0474 | 1.06 |
Preservative*CoolTemp | 0.0067 | 0.0034 | 0.0472 | 1.05 |
VacuumPress*ContaminationLevel | -0.0430 | -0.0215 | 0.0469 | 1.04 |
VacuumPress*CoolTemp | -0.0115 | -0.0058 | 0.0465 | 1.02 |
ContaminationLevel*CoolTemp | 0.1573 | 0.0786 | 0.0467 | 1.02 |
In these results, the coefficients for the main effects of Preservative, VacuumPress, and ContaminationLevel are positive numbers. The coefficient for the main effect of CoolTemp is a negative number. Generally, positive coefficients make the event more likely and negative coefficients make the event less likely as the value of the term increases.
Source | DF | Adj Dev | Adj Mean | Chi-Square | P-Value |
---|---|---|---|---|---|
Model | 10 | 46.2130 | 4.6213 | 46.21 | 0.000 |
Preservative | 1 | 22.6835 | 22.6835 | 22.68 | 0.000 |
VacuumPress | 1 | 7.3313 | 7.3313 | 7.33 | 0.007 |
ContaminationLevel | 1 | 9.6209 | 9.6209 | 9.62 | 0.002 |
CoolTemp | 1 | 1.3441 | 1.3441 | 1.34 | 0.246 |
Preservative*VacuumPress | 1 | 0.0608 | 0.0608 | 0.06 | 0.805 |
Preservative*ContaminationLevel | 1 | 0.5780 | 0.5780 | 0.58 | 0.447 |
Preservative*CoolTemp | 1 | 0.0051 | 0.0051 | 0.01 | 0.943 |
VacuumPress*ContaminationLevel | 1 | 0.2106 | 0.2106 | 0.21 | 0.646 |
VacuumPress*CoolTemp | 1 | 0.0153 | 0.0153 | 0.02 | 0.902 |
ContaminationLevel*CoolTemp | 1 | 2.8475 | 2.8475 | 2.85 | 0.092 |
Error | 5 | 0.9674 | 0.1935 | ||
Total | 15 | 47.1804 |
In these results, the main effects for Preservative, VacuumPress, and ContaminationLevel, are statistically significant at the at the α = 0.05 significance level. You can conclude that changes in these variables are associated with changes in the response variable.
The interaction terms are not statistically significant. The relationship between each variable and the response may not depend on the value of the other variable.
Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.
Unit of Change | Odds Ratio | 95% CI | |
---|---|---|---|
Dose (mg) | 0.5 | 6.1279 | (1.7218, 21.8087) |
In these results, the model uses the dosage level of a medicine to predict the presence or absence of bacteria in adults. In this example, the absence of bacteria is the Event. Each pill contains a 0.5 mg dose, so the researchers use a unit change of 0.5 mg. The odds ratio is approximately 6. For each additional pill that an adult takes, the odds that a patient does not have the bacteria increase by about 6 times.
For categorical predictors, the odds ratio compares the odds of the event occurring at 2 different levels of the predictor. Minitab sets up the comparison by listing the levels in 2 columns, Level A and Level B. Level B is the reference level for the factor. Odds ratios that are greater than 1 indicate that the event is more likely at level A. Odds ratios that are less than 1 indicate that the event is less likely at level A. For information on coding categorical predictors, go to Coding schemes for categorical predictors.
Level A | Level B | Odds Ratio | 95% CI |
---|---|---|---|
Month | |||
2 | 1 | 1.1250 | (0.0600, 21.0834) |
3 | 1 | 3.3750 | (0.2897, 39.3165) |
4 | 1 | 7.7143 | (0.7461, 79.7592) |
5 | 1 | 2.2500 | (0.1107, 45.7172) |
6 | 1 | 6.0000 | (0.5322, 67.6397) |
3 | 2 | 3.0000 | (0.2547, 35.3325) |
4 | 2 | 6.8571 | (0.6556, 71.7169) |
5 | 2 | 2.0000 | (0.0976, 41.0019) |
6 | 2 | 5.3333 | (0.4679, 60.7946) |
4 | 3 | 2.2857 | (0.4103, 12.7323) |
5 | 3 | 0.6667 | (0.0514, 8.6389) |
6 | 3 | 1.7778 | (0.2842, 11.1200) |
5 | 4 | 0.2917 | (0.0252, 3.3719) |
6 | 4 | 0.7778 | (0.1464, 4.1326) |
6 | 5 | 2.6667 | (0.2124, 33.4861) |
In these results, the categorical predictor is the month from the start of a hotel's busy season. The response is whether or not a guest cancels a reservation. In this example, a cancellation is the Event. The largest odds ratio is approximately 7.71, when level A is month 4 and level B is month 1. This indicates that the odds that a guest cancels a reservation in month 4 is approximately 8 times higher than the odds that a guest cancels a reservation in month 1.
Many of the model summary and goodness-of-fit statistics are affected by how the data are arranged in the worksheet and whether there is one trial per row or multiple trials per row. The Hosmer-Lemeshow test is unaffected by how the data are arranged and is comparable between one trial per row and multiple trials per row. For more information, go to How data formats affect goodness-of-fit in binary logistic regression.
The higher the deviance R^{2}, the better the model fits your data. Deviance R^{2} is always between 0% and 100%.
Deviance R^{2} always increases when you add additional terms to a model. For example, the best 5-term model will always have an R^{2} that is at least as high as the best 4-term model. Therefore, deviance R^{2} is most useful when you compare models of the same size.
The data arrangement affects the deviance R^{2} value. The deviance R^{2} is usually higher for data with multiple trials per row than for data with a single trial per row. Deviance R^{2} values are comparable only between models that use the same data format.
Goodness-of-fit statistics are just one measure of how well the model fits the data. Even when a model has a desirable value, you should check the residual plots and goodness-of-fit tests to assess how well a model fits the data.
Use adjusted deviance R^{2} to compare models that have different numbers of terms. Deviance R^{2} always increases when you add a term to the model. The adjusted deviance R^{2} value incorporates the number of terms in the model to help you choose the correct model.
Use AIC, AICc, and BIC to compare different models. For each statistic, smaller values are desirable. However, the model with the smallest value for a set of predictors does not necessarily fit the data well. Also use goodness-of-fit tests and residual plots to assess how well a model fits the data.
Deviance R-Sq | Deviance R-Sq(adj) | AIC | AICc | BIC |
---|---|---|---|---|
97.95% | 76.75% | 105.98 | 171.98 | 114.48 |
In these results, the model explains 97.95% of the total deviance in the response variable. For these data, the Deviance R^{2} value indicates the model provides a good fit to the data. If additional models are fit with different predictors, use the adjusted Deviance R^{2} value, the AIC value, the AICc value, and the BIC value to compare how well the models fit the data.
If the deviation is statistically significant, you can try a different link function or change the terms in the model.
Variable | Value | Count | Event Name |
---|---|---|---|
Spoilage | Event | 506 | Event |
Non-event | 7482 | ||
Containers | Total | 7988 |
Test | DF | Chi-Square | P-Value |
---|---|---|---|
Deviance | 5 | 0.97 | 0.965 |
Pearson | 5 | 0.97 | 0.965 |
Hosmer-Lemeshow | 6 | 0.10 | 1.000 |
In these results, alll of the goodness-of-fit tests have p-values higher than the usual significance level of 0.05. The tests do not provide evidence that the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict.