Function to optimize slope, offset and sd for all lines of fixations (extended from original paper)

This function uses many slopes, ver_offsets, sds for every lines, and use sum(min y_diff) as target measure for optimizationuses

cat_lines4(
  params,
  fit_it = TRUE,
  data,
  start_pts,
  k_bounds,
  o_bounds,
  s_bounds,
  den_sd_cutoff,
  den_ratio_cutoff,
  num_checkFirst = 5,
  num_checkLast = 10
)

Arguments

params

A vector of parameters for optimization, the three values in it refer to slope, offset, and sd

fit_it

A bollean variable; if it is TRUE, the function will return fit measure; if it is FALSE, the function will return fit information

data

A data.frame storing the fixation data including at least the x_pos and y_pos of each fixation

start_pts

A data.frame containing the starting position of each text line. It has three columns:

1. x_pos: x position of the first word in each text line.

2. y_pos: y position of the first word in each text line.

3. trial_num: the trial number of the current start_pts

k_bounds

A list containing the lower and upper boundaries of slope; default value is [-0.1, 0.1]

o_bounds

A list containing the lower and upper boundaries of offset; defaul value is [-0.5*dist of adjacent text lines, 0.5*dist of adjacent text line])

s_bounds

A list containing the lower and upper boundaries of sd; default value is [1, 20]

den_sd_cutoff

A float variable for cutoff threshold for density; If it is Inf, use mean(inv_dnorm(exp(data_den_max))) + 3*sd(inv_dnorm(exp(data_den_max))) as cutoff (99.7% are accepted)

den_ratio_cutoff

A float variable for cutoff threshold for density ratio (ratio between the maximum density and second maximum density)

num_checkFirst

An integer denoting the number of starting fixations used for checking start-reading bound; default value is 5

num_checkLast

An integer denoting the number of ending fixations used for checking end-reading bound; default value is 10

Value

A data.frame including fixation data, and fitting data including fit measures and fitted lines information. It adds the following columns:

1. line: Text line that each fixation belongs to

2. y_line: y position of the text line that each fixation is assigned to

3. y_res: Residualized y position of each fixation y_line + y_res will give the original y position of each fixation

4. slope: Optimized slope value for the fitted line that current fixation belongs to

5. offset: Optimizaed offset value for the fitted line that current fixation belongs to

6. sd: Optimized sd value for the fitted line that current fixation belongs to

7. fit_den: fitted density value for the fitted line that current fixation belongs to

8. fit_y_diff: fitted y difference for the fitted line that current fixation belongs to (accumulated y differences between each fixation and fitted lines)

Details

This function uses many slopes, ver_offsets, sds for every lines, and use sum(min y_diff) as target measure for optimizationuses

Author

Tao Gong gtojty@gmail.com