A COMPUTER IMPLEMENTED METHOD FOR ESTIMATING A READING SPEED OF AN INDIVIDUAL

Abstract

A computer-implemented method for estimating a reading speed of an individual. The method comprises the steps of: providing a reading speed model, based on a reading speed function comprising a set of parameters and a set of metrics; determining a printed stimulus to be presented to the individual by way of a reading run of a reading test and determining one or more stimulus features associated therewith; controlling an administration of the reading test to the individual based on the one or more determined stimulus features; receiving reading speed observation data based on the presented printed stimulus and corresponding to one or more responses made by the individual in the reading test.

Claims

1. A computer implemented method for estimating a reading speed curve of an individual, comprising the steps of: at a computing device including one or more processors and one or more input and/or output elements, providing a reading speed model, based on a reading speed function comprising a set of parameters and a set of metrics; determining a printed stimulus to be presented to the individual by way of a run of a reading test and determining one or more stimulus features associated therewith; controlling an administration of the run of the reading test to the individual based on the one or more determined stimulus features; wherein the reading speed function is configured to characterize the reading speed of the individual over a range of the one or more stimulus features of the presented printed stimulus, thus representing a reading curve for the individual, and to mimic at least part of a run of the administered reading speed test, and receiving reading speed observation data based on the presented printed stimulus and corresponding to one or more responses made by the individual in the reading test; wherein the method comprises an adaptive phase of: fitting the reading speed model to the received observation data such that the set of parameters and/or of metrics of the reading speed model and/or stimulus features is updated based on the reading speed observation data, to update the estimated reading speed of the individual; iterating the providing, the determining, the controlling, the receiving and the fitting according to stopping criteria to adaptively refine the estimated reading speed for the individual for a plurality of subsequent administrations of reading runs of the reading test; characterized in that before the adaptive phase, providing the reading speed model comprises a step of mapping out the reading speed function for the currently tested individual, by executing a preliminary administration of reading runs of the reading test to the individual based on presentation of printed stimuli having predetermined values of the one or more features; and by consequently receiving reading speed data to obtain a corresponding number of points on the reading curve.

2. The computer implemented method of claim 1, wherein the presented printed stimulus is a sentence.

3. The computer implemented method of claim 1, wherein providing the reading speed model comprises a step of defining the range of the one or more stimulus features and identifying a pre-defined number of predetermined values within the range of the one or more stimulus features to divide the range into corresponding portions.

4. The computer implemented method of claim 3, wherein the portions of predetermined values are substantially equal.

5. The computer implemented method of claim 1, wherein one of the features of the presented printed stimulus is print size.

6. The computer implemented method of claim 5, wherein providing the reading speed model comprises a step of calculating, by the reading speed function, adjusted reading speeds for each of the identified predetermined values of print size; and of counting the number of errors which the individual makes when reading at each of the identified predetermined values of print size.

7. The computer implemented method of claim 6, wherein the reading speed function corresponds to a logistic reading speed model, according to the following distribution $f\left(x_j\right)=\frac{\varphi }{1+\exp \left[-a\left(x_j-b\right)\right]}$ wherein: ϕ is a metric corresponding to the maximum reading speed on the reading curve for the individual (that is, the individual's reading speed when reading is not limited by print size); a is the rate of change from 0 to ϕ on the reading curve; and b is the inflection point of the reading curve.

8. The computer implemented method of claim 7, wherein providing the reading speed model comprises a step of testing the individual by presenting printed stimuli starting at the largest predetermined value of print size of the range and a step of receiving reading speed observation data to obtain a first observed value of the initial reading speed, thus obtaining a point on the reading curve corresponding to such largest predetermined value print size of the range.

9. The computer implemented method of claim 8, wherein providing the reading speed model comprises a step of providing check criteria based respectively on a cutoff error value for the number of errors which the individual makes at a given print size value; and on a cutoff speed value for the adjusted reading speed at a given print size value.

10. The computer implemented method of claim 9, wherein the cutoff speed value for the adjusted reading speed at a given print size value is a percentage of the first observed value of the initial reading speed.

11. The computer implemented method of claim 10, wherein providing the reading speed model comprises a step of comparing respectively the number of errors which the individual makes at a given print size value to the cutoff error value, wherein a first check criterion is met if the number of errors is less than or equal to the cutoff error value; and of comparing the adjusted reading speed at a given print size value to the cutoff speed value, wherein a second check criterion is met if the adjusted reading speed is equal or above the cutoff speed value.

12. The computer implemented method of claim 11, wherein providing the reading speed model comprises, if both check criteria are met, a step of reducing the print size value to the next smaller predetermined value; a step of testing the individual by presenting printed stimuli at the next smaller predetermined value of print size; and a step of comparing respectively the number of errors which the individual makes at the next smaller predetermined value of print size to the cutoff error value; and of comparing the adjusted reading speed at the next smaller predetermined value of print size to the cutoff speed value.

13. The computer implemented method of claim 12, wherein, if no further smaller predetermined value of print size exists, the reading speed observation data and the errors made by the individual when reading at each of the identified predetermined values of print size are stored for completing the provision of the reading speed model.

14. The computer implemented method of claim 11, wherein providing the reading speed model comprises, if either of the check criteria is not met, the step of increasing the print size value by a predefined amount with respect to the current print size value, if possible within the range of predetermined values of print sizes; the step of testing the individual by presenting printed stimuli at the corresponding increased print size value; and of comparing respectively the number of errors which the individual makes at the corresponding increased print size value to the cutoff error value, and of comparing the adjusted reading speed at corresponding increased print size value to the cutoff speed value.

15. The computer implemented method of claim 14, comprising the step of, if both check criteria are met, storing the reading speed observation data and the errors made by the individual when reading at each of the values of print size, for completing the provision of the reading speed model; otherwise, if either of the check criteria is not met, comprising the step of further increasing the print size value by a predefined amount with respect to the current print size value, up to the last print size value wherein both check criteria were met.

16. The computer implemented method of claim 14, comprising the step of repeating the testing of the individual at the largest predetermined value of print size of the range, if either of the check criteria is not met already when testing the individual by presenting printed stimuli starting at the largest predetermined value of print size of the range; and, if either of the check criteria is again not met, comprising the step of not proceeding to the adaptive phase.

17. The computer implemented method of claim 16, comprising the step of, irrespective of observation scenario/outcome whether the check criteria were met or whether the check criteria were not met, storing the reading speed observation data and the errors made by the individual when reading at each of the values of tested print sizes in a final data set, in order to complete the provision of the reading speed model.

18. The computer implemented method of claim 17, wherein the first iteration step of adaptively fitting the provided reading speed model to received observation data is based on fitting the provided reading speed model to the observation data.

19. The computer implemented method of claim 18, wherein adaptively fitting the provided reading speed model to received observation data corresponding to subsequent administrations of reading runs of the reading test to the individual comprises the step of defining a fitting function, comprising the reading speed function, and the step of optimizing the log posterior for the defined fitting function, to adaptively estimate the set of parameters and the set of metrics of the reading speed model.

20. The computer implemented method of claim 19, wherein the set of parameters and the set of metrics of the reading speed model thus estimated are used to calculate fitted adjusted reading speeds for each available print size.

21. The computer implemented method of claim 1, wherein the stopping criteria for the iterations of adaptively fitting the provided reading speed model to received observation data are based on cutoff values for estimated metrics, preferably on the posterior standard deviation, or standard errors, or the respective estimates thereof or on a combination of the standard errors.

22. The computer implemented method of claim 21, wherein the stopping criteria are based on cutoff values for the maximum reading speed, or MRS, and for the critical print size, or CPS.

23. The computer implemented method of claim 1, wherein adaptively fitting the provided reading speed model to received observation data corresponding to subsequent administrations of reading runs of the reading test to the individual comprises the step of controlling the print size of the next/subsequently administered printed stimulus, so that a corresponding point is obtained on the reading curve in a targeted position.

24. The computer implemented method of claim 23, wherein choosing the corresponding point on the reading curve lies within a subset of a parameter or metric space for one of the parameters or metrics of the reading speed model, such as for the maximum reading speed, or MRS.

25. The computer implemented method of claim 24, wherein the print size of the next/subsequently administered printed stimulus is selected in blocks of five distinct print size values, so that corresponding, distinct points are obtained in respective targeted positions of the reading curve, such as on an elbow, on a slope, and/or on a plateau of the reading curve, preferably corresponding to respective percentages (e.g. 90%; 25%-90%; 5%-25%, 90%-100%) of the maximum reading speed, or MRS.

26. The computer implemented method of claim 25, wherein the one or more responses made by the individual in the reading test are assessed by voice recognition software, both for reporting reading time and for counting errors.

27. A system comprising: a computing device including: one or more processors; one or more input and/or output elements; memory; and one or more programs stored in the memory, the one or more programs including instructions for: providing a reading speed model, based on a reading speed function comprising a set of parameters and a set of metrics, determining a printed stimulus to be presented to the individual by way of a reading run of a reading test and determining one or more stimulus features associated therewith; controlling an administration of the run of the reading test to the individual based on the one or more determined stimulus features; wherein the reading speed function is configured to characterize the reading speed of the individual over a range of the one or more stimulus features of the presented printed stimulus, thus representing a reading curve for the individual, and to mimic at least part of a run of the administered reading speed test, and receiving reading speed observation data based on the presented printed stimulus and corresponding to one or more responses made by the individual in the reading test; the one or more programs comprising an adaptive phase including instructions for: adaptively fitting the reading speed model to the received observation data such that the set of parameters and/or of metrics of the reading speed model and/or stimulus features is updated based on the reading speed observation data, to update the estimated reading speed of the individual; iterating the providing, the determining, the controlling, the receiving and the fitting according to stopping criteria to adaptively refine the estimated reading speed for the individual for a plurality of subsequent administrations of reading runs of the reading test; the one or more programs comprising instructions, to be executed before the adaptive phase, for mapping out the reading speed function for the currently tested individual in order to provide the reading speed model, by executing a preliminary administration of reading runs of the reading test to the individual based on presentation of printed stimuli having predetermined values of the one or more features; and by consequently receiving reading speed data to obtain a corresponding number of points on the reading curve.

28. A non-transitory computer-readable storage medium storing one or more programs configured to be executed by one or more processors of an electronic device with one or more input and/or output elements, the one or more programs including instructions for: providing a reading speed model, based on a reading speed function comprising a set of parameters and a set of metrics; determining a printed stimulus to be presented to the individual by way of a reading run of a reading test and determining one or more stimulus features associated therewith; controlling an administration of the run of the reading test to the individual based on the one or more determined stimulus features; wherein the reading speed function is configured to characterize the reading speed of the individual over a range of the one or more stimulus features of the presented printed stimulus, thus representing a reading curve for the individual, and to mimic at least part of a run of the administered reading speed test, and receiving reading speed observation data based on the presented printed stimulus and corresponding to one or more responses made by the individual in the reading test; the one or more programs comprising an adaptive phase including instructions for: adaptively fitting the reading speed model to the received observation data such that the set of parameters and/or of metrics of the reading speed model and/or stimulus features is updated based on the reading speed observation data, to update the estimated reading speed of the individual; iterating the providing, the determining, the controlling, the receiving and the fitting according to stopping criteria to adaptively refine the estimated reading speed for the individual for a plurality of subsequent administrations of reading runs of the reading test; the one or more programs comprising instructions, to be executed before the adaptive phase, for mapping out the reading speed function for the currently tested individual in order to provide the reading speed model, by executing a preliminary administration of reading runs of the reading test to the individual based on presentation of printed stimuli having predetermined values of the one or more features; and by consequently generating and receiving reading speed data to obtain a corresponding number of points on the reading curve.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The method and the system and according to the invention are described in more detail herein below by way of exemplary embodiments and with reference to the attached drawings, in which:

[0076] FIG. 1 illustrates an exemplary known reading curve, wherein reading speed is mapped out as a function of stimuli print size for a tested individual, highlighting some of the metrics which are referenced and used in some embodiments of the method for estimating a reading speed of an individual according to the present invention;

[0077] FIG. 2 illustrates an exemplary sequence of phases in an implementation of a method for estimating a reading speed of an individual according to the present invention;

[0078] FIG. 3 illustrates an exemplary work-flow of a preliminary phase of an embodiment of the method for estimating a reading speed of an individual according to the present invention; and

[0079] FIG. 4 illustrates an exemplary work-flow of an adaptive phase of the embodiment of FIG. 3, wherein the adaptive phase is subsequent to the preliminary phase.

DESCRIPTION OF EMBODIMENTS

[0080] In the following description certain terms are used for reasons of convenience and are not intended to limit the invention. The terms “right”, “left”, “up”, “down”, “under” and “above” refer to directions in the figures. The terminology comprises the explicitly mentioned terms as well as their derivations and terms with a similar meaning. Also, spatially relative terms, such as “beneath”, “below”, “lower”, “above”, “upper”, “proximal”, “distal”, and the like, may be used to describe one element's or feature's relationship to another element or feature as illustrated in the figures. These spatially relative terms are intended to encompass different positions and orientations of the devices in use or operation in addition to the position and orientation shown in the figures. For example, if a device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be “above” or “over” the other elements or features. Thus, the exemplary term “below” can encompass both positions and orientations of above and below. The devices may be otherwise oriented (rotated 90 degrees or at other orientations), and the spatially relative descriptors used herein interpreted accordingly. Likewise, descriptions of movement along and around various axes include various special device positions and orientations.

[0081] To avoid repetition in the figures and the descriptions of the various aspects and illustrative embodiments, it should be understood that many features are common to many aspects and embodiments. Omission of an aspect from a description or figure does not imply that the aspect is missing from embodiments that incorporate that aspect. Instead, the aspect may have been omitted for clarity and to avoid prolix description. In this context, the following applies to the rest of this description: If, in order to clarify the drawings, a figure contains reference signs which are not explained in the directly associated part of the description, then it is referred to previous or following description sections. Further, for reason of lucidity, if in a drawing not all features of a part are provided with reference signs it is referred to other drawings showing the same part. Like numbers in two or more figures represent the same or similar elements.

[0082] The following description sets forth exemplary systems, devices, methods, parameters, and the like. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure but is instead provided as a description of exemplary embodiments. For example, reference is made to the accompanying drawings in which it is shown, by way of illustration, specific example embodiments. It is to be understood that changes can be made to such example embodiments without departing from the scope of the present disclosure.

[0083] As used herein, the terms “subject” or “individual” are equivalent to the term “patient” and refer to a mammalian organism, preferably a human being, who may be diseased with the condition (e.g., disease or disorder) of interest and who may benefit biologically, medically, or in quality of life from treatment for the condition.

[0084] With initial reference to FIGS. 1 and 2, the computer implemented method for estimating a reading speed of an individual according to the present invention substantially aims at characterizing the reading speed of the individual over a range of one or more stimulus features, such as print sizes, of printed stimuli which are subsequently presented to an individual during respective runs of a reading test.

[0085] FIG. 1 is an example of a prexisting reading curve, drawn from “Baseline MNREAD Measures for Normally Sighted Subjects From Childhood to Old Age” by Calabrese et al., published in “Investigative Ophthalmology & Visual Science”, 2016. In the Figure, the x-axis is print size as measured by log MAR, and the Y axes show reading time in seconds and reading speed in words per minute. A minimum reading acuity is shown to be −0.2 log MAR whilst a critical print size (below which reading speed is impaired) is 0.0 log MAR. The hatched band, between 0.4 and 1.3 log MAR represents a range of the ten largest print sizes on the standard MNREAD chart.

[0086] The ultimate goal of the method according to the present invention is estimating a reading curve representative of the reading performance of the tested individual, mimicking at least part of a run of the administered reading speed test, such as the reading curve shown in FIG. 1, wherein reading speed is mapped out as a function of stimuli print size for the tested individual.

[0087] As shown in FIG. 2, the method for estimating a reading speed of a tested individual according to the present invention overall comprises a sequence of steps performing a preliminary phase; a successive sequence of steps configured to perform an adaptive phase; and a final sequence of steps aimed at delivering a reading curve specifically obtained for the tested individual, in a form similar to the one shown in FIG. 1.

[0088] The gist of an administration of the reading test to the individual in the preliminary phase, based on presentation of printed stimuli having predetermined and targeted values of print sizes, is to preliminarily approximate the actual shape and position of the reading curve for the currently tested individual, in a way that the successive adaptive phase quickly converges to yield a reading curve best characterizing the reading performance of the tested individual.

[0089] In some embodiments a selection of print sizes are chosen in a preliminary phase of the method for estimating a reading speed of a tested individual according to the present invention, wherein for each of the print sizes observation data is obtained which correspond to respective adjusted reading speeds for the tested individual and are representative of respective points on a reading curve specific to the tested individual. In some embodiments, the five print sizes are selected, at equal points between −0.10 log MAR to 1.3 log MAR.

[0090] In connection with each of such predetermined values of print size, corresponding points representative of adjusted reading speeds of the tested individual have been obtained. The adjusted reading speeds can be calculated by a reading speed function. Also, the number of errors made by the tested individual when reading at each of the predetermined print sizes is counted and recorded.

[0091] For example, if the minimum print size is set to −0.10 log MAR and the maximum print size is 1.3 log MAR, with five initial points, the print sizes at which data are collected, both in terms of reading speed and errors made, are 1.3 log MAR, 0.95 log MAR, 0.60 log MAR, 0.25 log MAR, and −0.1 log MAR.

[0092] Reference will be made to the work-flow capturing the sequence of steps of the preliminary phase of FIG. 3, wherein the succession of steps has been previously explained in the disclosure of the invention. The reading speed at the maximum print size is referred to as the individual's initial reading speed. This is obtained by presenting printed stimuli to the tested individual starting at the largest predetermined value of print size of the range, namely 1.3 log MAR for the specific case exemplified. Corresponding reading speed observation data are received, to obtain a first observed value of the initial reading speed. A first point on the reading speed curve is obtained, resulting in an adjusted reading speed corresponding, for example, to a value of print size equal to 1.3 log MAR.

[0093] After obtaining the data at the initial, e.g. largest, print size, test criteria are checked. These test check criteria are based respectively on a cutoff error value for the number of errors which the individual makes at a given print size value; and on a cutoff speed value for the adjusted reading speed at a given print size value. For instance, the cutoff speed value for the adjusted reading speed at a given print size value can be set to a percentage of the first observed value of the initial reading speed at 1.3 log MAR.

[0094] The number of errors which the individual makes at 1.3 log MAR is compared to the cutoff error value. A first check criterion is met if the number of errors is less than or equal to the cutoff error value. If the tested individual makes more errors than the cutoff error value, then the tested individual has to read another sentence at the largest print size, e.g. at 1.3 log MAR. If the number of errors newly exceeds the cutoff error value, then the reading test ends for this tested individual and does not proceed to the subsequent adaptive phase. Both observations at the maximum print size are saved in a final data set.

[0095] If, instead, in this new observation the number of errors is less than the cutoff error value, then the reading speed of this observation becomes the initial reading speed and the test proceeds to the next print size, which is 0.95 log MAR in the given example.

[0096] If the tested individual reads the presented sentence at 0.95 log MAR and meets both check criteria, observations are added to the final data set and the test proceeds to the next smaller predetermined value of print size, namely 0.60 log MAR.

[0097] If at 0.60 log MAR the tested individual makes, for instance, more errors than the cutoff or reads slower than the cutoff speed value, this leads to the individual having to take the test with printed stimuli having a print size value increased by a predefined amount. Such predefined amount, or step-up interval, can be of +0.05 log MAR or of +0.1 log MAR, with respect to the current print size value. Thus, 0.95 log MAR becomes the new maximum print size, at which check criteria were met.

[0098] Therefore, the tested individual will have to take the test a print size of, e.g., 0.70 log MAR. If the observation data at 0.70 log MAR meets the check criteria, then the preliminary phase is deemed complete for the tested individual. If, however, the check criteria are not met at 0.70 log MAR, then the current print size value is further incremented by a predefined amount. Observation data are, for instance, obtained for a print size of the presented stimuli of 0.80 log MAR. If, once again, the observation does not meet the criteria, then a final observation is taken at 0.90 log MAR, which is below the new maximum print size at which the test was last successful, that is 0.95 log MAR.

[0099] After reading the sentence at 0.90 log MAR, and registering the relative observation data, the initial phase for the tested individual would end, since a newly incremented print size would equal or exceed the new maximum print size.

[0100] Irrespective of observation scenario/outcome, whether the check criteria were met or whether the check criteria were not met, the method according to the present invention can comprise the step of storing the reading speed observation data and the errors made by the individual when reading at each of the values of tested print sizes in a final data set, in order to complete the provision of the reading speed model achieved during the preliminary phase.

[0101] In the embodiment hereby exemplified, the minimum number of observations an individual can have is two, when the individual fails twice at the maximum print size, and the remainder of the test is not completed (i.e. the adaptive phase is not entered). Conversely, the minimum number of observations an individual can have in a successful preliminary phase is three.

[0102] As shown in FIG. 2, the preliminary phase is generally followed by the adaptive phase, then by acquisition of the final reading curve. The first iteration step of fitting the provided reading speed model to received observation data is based on fitting the provided reading speed model to the observation data obtained by implementing the preliminary phase and stored in the abovementioned final data set.

[0103] The first iteration step is then followed by further steps of fitting the provided reading speed model to received observation data corresponding to subsequent administrations of reading runs of the reading test to the individual. To this purpose, a fitting function is defined, comprising the reading speed function, and the log posterior for the defined fitting function is optimized, to estimate the set of parameters and the set of metrics of the reading speed model. The estimates for the set of parameters and/or of metrics of the reading speed model are adaptively updated, based on the reading speed observation data progressively received. The set of parameters and the set of metrics of the reading speed model thus estimated are used to calculate fitted adjusted reading speeds for each available print size.

[0104] A logistic model equation is used to create the reading speed function ƒ(x.sub.j), formulated as

[00005]$\frac{\varphi }{1+\exp \left[-a\left(x_j-b\right)\right]}.$

[0105] y.sub.j can be set as the adjusted reading speed at the corresponding print size, x.sub.j. y.sub.j substantially characterizes the reading curve which the reading speed model according to the present invention intends to produce.

[0106] As already explained, y.sub.j can be assumed to have a normal distribution according to the following exemplary expression:

[00006]$y_j\sim N\left(\frac{\varphi }{1+\exp \left[-a\left(x_j-b\right)\right]},\sigma \right)$

wherein the mean is defined by the above logistic model equation.

[0107] Parameter values of ϕ, a, and b of the logistic model equation that maximize the log posterior distribution are then used as updated estimates for ϕ, a, and b. In general terms, the optimization of the log posterior distribution has been described in the disclosure of the invention.

[0108] Stopping criteria for the iterations of adaptively fitting the provided reading speed model to received observation data are based on cutoff values for the posterior standard deviation of the maximum reading speed, or MRS, and for the critical print size, or CPS.

[0109] The posterior standard deviation of these metrics are calculated based on a number of samples from the approximate normal posterior distribution. The Hessian matrix of the log-posterior distribution is numerically estimated, and the samples are drawn from a multivariate normal distribution with the mean being the parameter estimates, and the covariance matrix being the inverse of the Hessian matrix. For each of the draws of the parameters, MRS and CPS are calculated. The posterior standard deviation of these metrics would then be the standard deviation of all MRS and CPS values. The stopping criteria can depend on some combination of the standard errors for MRS and CPS, or on just one of the standard errors.

[0110] If the stopping criteria are not met, subsequent administrations of reading runs of the reading test to the individual are envisaged, wherein the print size of the next/subsequently administered printed stimulus is controlled, so as to achieve that a corresponding point is obtained on the reading curve in a targeted position.

[0111] As evident from FIG. 4, the print size of the next/subsequently administered printed stimulus is adaptively selected in blocks of five distinct print size values, so that corresponding, distinct points are obtained in respective targeted positions of the reading curve, such as on an elbow, on a slope, and/or on a plateau of the reading curve. Alternatively, blocks of three distinct print sizes have been further tested.

[0112] These targeted positions can correspond to respective percentages of the maximum reading speed, or MRS. By way of example, a first print size can be selected corresponding to 90% of the MRS estimate, in order to obtain a point on the elbow of the reading curve. A second and/or third print size can be selected corresponding to a range of 25%-90% of the MRS estimate, to obtain respective points on an upper portion of the slope of the reading curve. A fourth print size can be chosen corresponding to a range of 5%-25% of the MRS estimate, so as obtain a point on a lower portion of the slope of the reading curve. Finally, a fifth print size can be selected corresponding to a range of 90%-100% of the MRS estimate to produce a point on a plateau of the reading curve.

[0113] Other schemes can be considered for adaptively locating the next optimal point. For instance, an adaptive scheme can allocate the next optimal point at the current estimate of some print size corresponding to simply one set percentage of the maximum reading speed, or MRS. For example, the print size corresponding to 80% of the MRS could be the next optimal print size for each iteration.

[0114] A different adaptive scheme can alternate between different percentages of MRS, based on what iteration number of the adaptive scheme has been reached. An example of this approach would let the next optimal print size vary between the print sizes corresponding to 99% of the MRS, 75% of the MRS, and 15% of the MRS. When the number of iterations is divided by four, the remainder determines what the next optimal print size is. If the remainder is zero, the next optimal print size is the print size corresponding to 99% of the MRS. If the remainder is one or two, the next optimal print size is that print size corresponding to 75% of the MRS, and if the remainder is three, the next optimal print size is the print size corresponding to 15% of the MRS. The aforementioned three percentages can be fixed or can be made to vary.

[0115] Also, a print size can be added corresponding to a point on the plateau of the reading curve, by choosing a print size that falls between the current estimate of CPS and the maximum print size. This can be helpful to obtain a more accurate estimate of MRS.

[0116] The last step in the adaptive cycle generates an adjusted reading speed at the optimal point and adds it to the final data set for the adaptive phase.

[0117] Once the function has cycled through the iterations of the adaptive phase until some stop criteria is met, it adds the observation to the final data set. The adaptive phase function returns the fits from each iteration of the adaptive phase, and the final data set from the adaptive phase.

[0118] Other aspects of the disclosed embodiments will be apparent to those skilled in the art from consideration of the specification and practice of the disclosed embodiments. It is intended that the specification and examples be considered as exemplary only, with exemplary scopes of the disclosed embodiments being indicated by the following exemplary claims comprising examples and embodiments of the invention.