The table below shows the model forms used for models. Seven forms are available. You can calculate and select from each of the regression equations to choose the best model.
Model Type | Model Form | Description |
---|---|---|
Exponential | y = a + becx | The pavement condition remains nearly constant for a number of years, and then rapidly deteriorates. |
Hyperbolic | y = a + 1 / (b + cx) | The pavement condition deteriorates steadily with the greatest rate of deterioration occurring in the early years. |
Inverse Exponential | y = a + becx | The pavement condition remains nearly constant for a number of years, and then rapidly deteriorates. |
Linear | y = a + bx | The rate of deterioration of the pavement condition is the same from year to year. |
Piecewise Linear | y = ai + bix | You specify up to six coordinates, and the system draws a straight line between each coordinate. This type allows you to specify points in time where the deterioration rate "jumps" to a new value, where it again remains constant until the next discontinuity. |
Power | y = a + bx^c | This type of model is a special form of the exponential type. Like an exponential-type graph, the pavement condition remains nearly constant for a large number of years, and then rapidly deteriorates. However, the rate of deterioration is based directly on time rather than a logarithm. |
Sigmoidal | y = a + (be(-c/x)^d) | The pavement condition remains nearly constant for a number of years, then rapidly deteriorates, and then remains nearly constant again. |
where:
y = condition attribute being predicted.
x = age (years).
a, b, c, and d = regression coefficients.
Linear regression is applied to the linear, exponential, inverse exponential, and hyperbolic types of models. To achieve a linear model form, two transformations are performed:
Model Type | Model Form | Linear Transformation |
---|---|---|
Linear | y = a + bx | None |
Exponential | y = a + becx | y'' = ln(y') |
Inverse Exponential | y = a + becx | y'' = ln(101 - y') |
Hyperbolic | y = a + 1 / (b + cx) | y'' = 1 / y' |
The general methodology for building performance models in the system is: