Generate an average curve using lm

The user must decide on a single dependent variable (Y) and a single independent variable (X). The user will specify a formula with the relationship between the dependent and independent variables. For a data.frame containing stress-strain (or load-deflection) data for more than one coupon, the maximum value of X for each coupon is found and the smallest maximum value determines the range over which the curve fit is performed: the range is from zero to this value. Only positive values of X are considered. For each coupon individually, the data is divided into a user-specified number of bins and averaged within each bin. The resulting binned/averaged data is then passed to stats::lm() to perform the curve fitting.

Usage

average_curve_lm(data, coupon_var, model, n_bins = 100)

Arguments

data

a data.frame

coupon_var

the variable for coupon identification

model

a formula for the curve to fit

n_bins

the number of bins to average the data inside into before fitting

Value

an object of class average_curve_lm with the following content:

• data the original data provided to the function

• binned_data the data after the binning/averaging operation

• fit_lm the results of the call to lm

• n_bins the number of bins specified by the user

• max_x the upper end of the range used for fitting

• y_var the independent (Y) variable

• x_var the dependent (X) variable

Details

When specifying the formula (argument model), there are two things to keep in mind. First, based on physical behavior, it is normally desirable to set the intercept to zero (e.g. so that there is 0 stress at 0 strain). To do this, include a term +0 in the formula. Second, when specifying a term for a power of the X variable (for example, $X^2$), this needs to be wrapped inside the "as-is" operator I(), otherwise, R will treat it as an interaction term, rather than an exponent. In other words, if you want to include a quadratic term, you need to write I(X^2) (replacing X with the appropriate variable from your data.frame).

See also

~, I(), lm(), average_curve_optim(), print.average_curve_lm(), summary.average_curve_lm(), augment.average_curve_lm()

Examples

# using the `pa12_tension` dataset and fitting a cubic polynomial with
# zero intercept:
curve_fit <- average_curve_lm(
  pa12_tension,
  Coupon,
  Stress ~ I(Strain) + I(Strain^2) + I(Strain^3) + 0,
  n_bins = 100
)
print(curve_fit)
#> 
#> Range: ` Strain ` in  [ 0,  0.1409409 ]
#> 
#> Call:
#> average_curve_lm(data = pa12_tension, coupon_var = Coupon, model = Stress ~ 
#>     I(Strain) + I(Strain^2) + I(Strain^3) + 0, n_bins = 100)
#> 
#> Coefficients:
#>   I(Strain)  I(Strain^2)  I(Strain^3)  
#>        1173        -8762        20481  
#> 
## Range: ` Strain ` in  [ 0,  0.1409409 ]
##
## Call:
##   average_curve_lm(data = pa12_tension, coupon_var = Coupon,
##                    model = Stress ~ I(Strain) + I(Strain^2) + I(Strain^3)
##                    + 0, n_bins = 100)
##
## Coefficients:
##    I(Strain)   I(Strain^2)   I(Strain^3)
##        1174         -8783         20586