1. A computer-implemented method of analyzing large scale survey results comprising: obtaining a sparse data set representing a subset of an original data set comprising a plurality of individuals' responses to a plurality of questions using a computer system, wherein the sparse data set comprises less than ninety percent of the responses in the original data set; analyzing the sparse data set using a diagnostic model using the computer system, the diagnostic model comprising multiple models according to an expression: P ⁡ ( X = x ❘ β i ⁢ ⁢ … ⁢ , a ⁢ ⁢ … ⁢ , q i ⁢ ⁢ … ⁢ , c ) = exp ⁡ [ β xic + ∑ k = 1 K ⁢ ⁢ x ⁢ ⁢ γ ikc ⁢ q ik ⁢ a k ] 1 + ∑ y = 1 m ⁢ ⁢ exp ⁡ [ β yic + ∑ k = 1 K ⁢ ⁢ y ⁢ ⁢ γ ikc ⁢ q ik ⁢ a k ] , wherein c is a number of observed groups ranging from 1 to an integer C, K is a number of attributes, a k are skill level parameters, i is an index for question items, q ik are parameters relating question items to skills, β xic and β yic are difficulty parameters for groups c=1,. .. , C, x is an observed item response, m is a number of response categories, and γ ikc are discrimination parameters for skill k and for groups c=1,. .. , C; said analyzing comprising generating a probability of given responses based upon difficulty parameters, skill levels, and parameters relating question items to skills; and obtaining, using the computer system, estimated person parameters indicative of an individual's ability as well as difficulty parameters and discrimination parameters, using the diagnostic model.