How did Jesus select the Apostles to witness the Transfiguration?

We read in Matthew, Mark and Luke how Jesus took Peter, James and John (last two being brothers) to witness the Transfiguration atop Mount Tabore. Peter would later be named the Rock on which Jesus' Church was to be built. John was the only apostle who stood by the Cross and was 'the disciples whom Jesus loved' according to himself. As for James,he does not find a special mention - favourable or otherwise- in the Gospels. Given that the nine Apostles left out would be prone to human envy, the Lord would have selected the three with utmost care, and with certain yardsticks. My question, therefore is: **Are there any apocryphal writings which mention the yardsticks, if any, adopted by Jesus in selecting the three apostles who would witness the Transfiguration?** Inputs from scholars of any denomination are welcome.