In our longitudinal study, we have been satisfied with SSRS for mothers and children.

But would check out newer options of we were to conduct the study today.

It's a good idea to get information from different informants. In my lab, we have used a number of different measures, but the ones detailed above are useful and well documented in the literature. We have also used Susan Harter's perceived competence scale, which has always given us good reliability. The SDQ is a standard measure used by school and clinical psychologists in the UK and it has proved to be of benefit when assessing certain groups. Hope that info is useful.

I would recommend the Harter Self Perception Profile surveys, by Susan Harter. They measure different dimensions of the self-concept related to perceived competence and self-importance (including the social domain). There are separate questionnaires for children, adolescents, college students, adults, older adults, and individuals with learning disabilities, with slightly different dimensions, based on relevance to a given age group. You could use these to look at social competence alone, or social competence compared to competence within other domains. You can also compare self-report with parent or teacher ratings.

These questionnaires are posted online for free. https://portfolio.du.edu/SusanHarter/page/44210

I use a combination of tools including a home "grown" one. I like the Conners as it has an early childhood component as well as a tool for children seven and above. But as it has been mentioned prior to my joining the conversation, the usefulness of rating scales is limited to what you are measuring. I like conducting interviews and asking questions about social competencies in different settings such as home, school, church and after school programs such as Boys Scouts/Girl Scouts, Boys and Girls Club or daycare. You can get a very skewed picture of a child by looking at only one or two settings thus I use a locally developed interview of social history as well as a functional behavior assessment questionnaire which also identifies the lagging social skills of children. You might try looking up the ALSUP. None of these tools are stand alone measures but in conjunction together they can shine light on social strengths and weaknesses. Another person who has researched in the area of social competencies is Brad Chapin in the realm of self-regulation. He has some VERY USEFUL tools that I use with parents looking for some on the spot helps that work.

I guess I would want to take a step back and ask, "competence to achieve what?" there are many possibilities: being a leader, being a bully who gets away with it, being liked by lots of people, being somebody people trust even though they are boring, a competent at manipulating adults to get what is wanted, being competent at not being bullied, being someone others want to play with, and so on; i.e. what is the goal/end point?. Then there is, "competence with whom?" peers, younger, older children, adults, teachers, parents, etc etc.

Sorry to add these complexities but it is clearly not a unitary concept. It is likely that children who are competent in one area are more likely to be competent in another, but that must be a finding, nor an assumption. One of the many things that holds psychology back from being a science and from finding out much interesting, is the assumption that it is appropriate to find "measures" of a priori concepts without knowing how to identify the thing itself. That is because psychology tends to start in the wrong place - from hypotheses plucked from common sense or theories similarly derived and not from solid detailed observation of the natural phenomena.

So my suggestion to you is, ask yourself why you want this "measure"? what are the natural phenomena you want to study? can you you split the idea up into chunks which are directly related top what is observable?

Good luck!