Preliminaries. 1. Download: bootstrap-software.org/psignifit. 2. Unzip, untar (e.g., in /Users/luke/psignifit)

Transcription

1 Using psignifit() psignifit(): a Matlab toolbox by J. Hill and F. Wichmann for fitting psychometric functions, bootstrapping confidence intervals, and statistics

2 Preliminaries 1. Download: bootstrap-software.org/psignifit 2. Unzip, untar (e.g., in /Users/luke/psignifit) 3. >> addpath( /Users/luke/psignifit ); >> help psignifit 4. See: psych_tool_demo.m 5. Cite: Wichmann & Hill (2001a, 2001b). Perception and Psychophysics

3 Preliminaries psignifit() implements maximum-likelihood fitting and parametric bootstrapping. Those papers (above) use MC simulation to explore the consequences of, e.g., sampling scheme, trials numbers, and the choice of the specific form of the psychometric function.

4 α, β, γ, λ Parameters

5 Parameters α, β, γ, λ Performance [prop. correct] 1 0 α, β Stimulus intensity [a.u.] λ γ

6 Example 1: Contrast Gain >> whos dat1 dat2 Name Size Bytes Class Attributes dat1 6x3 144 double dat2 6x3 144 double >> dat1 dat1 = >>% Three columns: stimulus intensity [a.u.]; performance [prop n]; num trials.

7 >> which plotpd /Users/luke/psignifit/plotpd.m >> plotpd(dat1, Color, black ); >> plotpd(dat2, Color, red ); Example 1: Contrast Gain

8 >> which plotpd /Users/luke/psignifit/plotpd.m >> plotpd(dat1, Color, black ); >> plotpd(dat2, Color, red ); Example 1: Contrast Gain

9 Example 1: Contrast Gain >> T1 = pfit(dat1,'shape',shapef,'n_intervals',n_interval,'cuts',... THRESH,'lambda_limits',[0 LAMBDA_UPPER]);

10 Example 1: Contrast Gain >> B = 2000; >> SHAPEF = weibull ; >> N_INTERVALS = 4; >> THRESH = [ ]; >> LAMBDA_UPPER = 0.05; >> % For more options, see help psych_options. >> T1 = pfit(dat1,'shape',shapef,'n_intervals',n_interval,'cuts',... THRESH,'lambda_limits',[0 LAMBDA_UPPER]);

11 Example 1: Contrast Gain >> B = 2000; >> SHAPEF = weibull ; >> N_INTERVALS = 4; >> THRESH = [ ]; >> LAMBDA_UPPER = 0.05; >> % For more options, see help psych_options. >> T1 = pfit(dat1,'shape',shapef,'n_intervals',n_interval,'cuts',... THRESH,'lambda_limits',[0 LAMBDA_UPPER]); psi(x) = gamma + (1 - gamma - lambda) * F(x, alpha, beta) using Weibull function for F and assuming 4AFC design (gamma = 0.25) lambda is constrained within [0, 0.05] fitting to original data initial: {alpha = , beta = , gamma = 0.25, lambda = 0.01} final: {alpha = , beta = , gamma = 0.25, lambda = } running 1999 simulations using fitted parameters Stats for generating distribution: D = , r_pd = , r_kd = random seed: seconds.... >> T2 = pfit(dat2,'shape',shapef,'n_intervals',n_interval,'cuts',... THRESH,'lambda_limits',[0 LAMBDA_UPPER]);...

12 >> plotpf(shapef,t1.params.est,'color','black','linewidth',4); >> plotpf(shapef,t2.params.est,'color','red','linewidth',4); Example 1: Contrast Gain

13 Example 1: Contrast Gain >> OFFSET_TH1 = 1/N_INTERVAL ; >> OFFSET_TH2 = 1/N_INTERVAL - 0.1; >> line(t1.thresholds.lims(:,2),offset_th1 *... ones(size(t1.thresholds.lims(:,2))),'color','black','linewidth',4); >> line(t2.thresholds.lims(:,2),offset_th2 *... ones(size(t2.thresholds.lims(:,2))),'color','red','linewidth',4);

14 Example 1: Contrast Gain >> T1 T1 = shape: 'Weibull' params: [1x1 struct] stats: [1x1 struct] thresholds: [1x1 struct] slopes: [1x1 struct] fisher: [4x4 double] sens: [1x1 struct] cuts: [ ] conf: [ ] conflimmethod: 'BCa' gen: [ ] R: 1999 randseed: e+09 est: [ ] cpe: [ ] deriv: [4x3 double] lff: [4x3 double] bc: [ ] acc: [ ] lims: [4x3 double] quant: [4x3 double] worst: [4x3 double] >>

15 >> T1.params ans = est: [ ] cpe: [ ] deriv: [4x4 double] lff: [4x4 double] bc: [ ] acc: [ ] lims: [4x4 double] quant: [4x4 double] worst: [4x4 double] >> T1.thresholds ans = est: [ ] cpe: [ ] deriv: [4x3 double] lff: [4x3 double] bc: [ ] acc: [ ] lims: [4x3 double] quant: [4x3 double] worst: [4x3 double] >> Example 1: Contrast Gain

16 Whatʼs going on? Discussion 1

17 Discussion 1

18 Discussion 1

19 >> whos dat3 dat4... >> plotpd(dat3, Color, black ); >> plotpd(dat4, Color, red ); Example 2: Response Gain

20 Example 2: Response Gain >> LAMBDA_UPPER = 0.75; >> T3 = pfit(dat3,'shape',shapef,'n_intervals',n_interval,'cuts',... [ ],'lambda_limits',[0 LAMBDA_UPPER]); psi(x) = gamma + (1 - gamma - lambda) * F(x, alpha, beta) using Weibull function for F and assuming 4AFC design (gamma = 0.25) lambda is constrained within [0, 0.75] fitting to original data initial: {alpha = , beta = , gamma = 0.25, lambda = 0.375} final: {alpha = , beta = , gamma = 0.25, lambda = } running 1999 simulations using fitted parameters Stats for generating distribution: D = , r_pd = , r_kd = random seed: seconds.... >>

21 >> plotpf(shapef,t3.params.est,'color','black','linewidth',4); >> plotpf(shapef,t4.params.est,'color','red','linewidth',4); Example 2: Response Gain

22 Example 2: Response Gain >> line(t3.thresholds.lims(:,2),offset_th1 *... ones(size(t3.thresholds.lims(:,2))),'color','black','linewidth',4);...

23 General Discussion >> help psych_options... Model options ============= #SHAPE The shape of the underlying psychometric distribution function F. supported values: Weibull, logistic, cumulative Gaussian, Gumbel, linear default: logistic

24 General Discussion >> help psych_options... Model options ============= #ALPHA_LIMITS, #ALPHA_PRIOR #BETA_LIMITS, #BETA_PRIOR #GAMMA_LIMITS, #GAMMA_PRIOR #LAMBDA_LIMITS, #LAMBDA_PRIOR The limits in which each of the parameters is allowed to vary.... The syntax #WHATEVER_LIMITS lo, hi is equivalent to #WHATEVER_PRIOR -flat lo, hi and the two options (_LIMITS and _PRIOR) cannot be applied simultaneously to the same variable.... #LAMBDA_PRIOR -gaussian mu, std implements a Gaussian prior with the given mean and standard deviation.

25 General Discussion >> help psych_options... Measures of interest ==================== #CONF Cumulative probability levels at which confidence interval boundaries are calculated: range (0, 1). default: [ ] (equivalent coverage to [ ] std's from the mean of a Normal)

26 General Discussion >> help psych_options... Measures of interest ==================== #CONF Cumulative probability levels at which confidence interval boundaries are calculated: range (0, 1). default: [ ] (equivalent coverage to [ ] std's from the mean of a Normal)

27 General Discussion

28 General Discussion