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I would like to estimate models with either the intercept (model a) or the slope (model b) are fixed, and also estimate unconstrained model (c), where each of these parameters was allowed to vary, and a null model (d), where none could. Then, I would like to compare them using Log-likelihood ratio test of BIC/AIC values (I don't know what's better).

Here is my code, but I don't know if it's appropriate. Note also that I consider here only 1 subject, but how to integrate this model comparison for several subjects?

I have reaction times for several conditions that I transformed into quantiles and then I use probate and reciprobit scales 'to normalize' them.

library(pracma)
library(lmtest)
library(ggplot2)
library(scales)

rt1 <- c(2343, 1411, 928, 767, 929, 775, 1008, 922, 1127, 1516, 904, 771, 1044, 974, 1096, 1688, 2018, 1726, 1523, 1910, 1186, 1287, 1220, 834, 1267,1827, 859, 835, 1729, 859, 1305, 1238, 1451, 756, 1331, 872, 729, 1053, 789, 982, 737, 1410, 865, 926, 885, 1026, 657, 1528, 1046, 930, 770, 936, 1019, 1156, 964, 1951, 783, 769, 1693, 775, 688, 913)

rt2 <- c(1143, 752, 1071, 1215, 698, 803, 751, 869, 679, 801, 830, 935, 794, 676, 960, 857, 873, 658, 918, 769, 649, 676, 829, 803, 672, 647, 756, 719, 558, 654, 854, 707, 676, 795, 632, 666, 764, 685, 699, 534, 547, 721, 837, 778, 608, 532, 564, 686, 830, 850, 577, 591, 630, 612, 728, 540, 785, 622, 538, 635, 606, 1083)

## Quantiles
qq1    = quantile(rt1,pp)
qq2    = quantile(rt2,pp)

qq1inv    = -1/qq1*1000
qq2inv    = -1/qq2*1000

## Probit scale
pp = c(1,2,3,5,6,seq(10,90,5),95,96,97,98,99)/100


## Create dataframe
inv_qquantile <- c(qq1inv,qq2inv)
pp_scale <- rep(pp,length.out=length(qquantile))
conditions <- c(rep('cond1',length.out=length(qq1inv)),rep('cond2',length.out=length(qq2inv))

dataall=data.frame(condition,inv_qquantile,pp_scale)

ggplot(dataall, aes(inv_qquantile,pp_scale,color=condition)) +
  geom_point() +
  scale_y_continuous(trans = probit_trans())+
  geom_smooth(method = lm,se=F)

The I have my 4 models:

## Estimate models

#-- slope fixed
a = glm(pp_scale ~ 0+inv_qquantile+condition,family = binomial(link = "probit"), dataall)

#-- intercept fixed
b = glm(pp_scale ~ inv_qquantile:condition,family = binomial(link = "probit"), dataall)

#-- unconstrained model
c = glm(pp_scale ~ inv_qquantile*condition,family = binomial(link = "probit"), dataall)

#-- null model
d = glm(pp_scale ~ 1,family = binomial(link = "probit"), dataall)

BIC(a)
BIC(b)
BIC(c)
BIC(d)
NelsonGon
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CaroleGE
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    Unless you have a strong theoretical justification (pretty rare!), you should never have an interaction in a model without also including its main effects. Similarly for a model without intercept. – Roland Jun 15 '20 at 11:54
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    Thank you for your comment. Actually my question is based on a theoretical framework of decision making model which interprets the reaction times according to different parameters (accumulation of evidence, or modification of the detection threshold). This estimation of the best model will allow me to interpret behavior changes according to my different conditions. – CaroleGE Jun 15 '20 at 12:07

0 Answers0