'Factor analysis' refers to statistical techniques developed for identification and characterisation of statistical constructs (also called as 'factors' or 'latent variables'). Statistical constructs are typically constructed of several variables or items that are measured directly and reflect, or associated with, the same aspect or attribute. Constructs are not normally measured directly (unlike the variables constructing them), which is why they are often termed as 'latent variables' characterised by their factor scores. Constructs or factors describe and quantify mutual characteristic(s) of the associated measured variables and represent those measured variables as an overarching general characteristic or attribute.
Here is a conceptual explanation of a construct or factor, which is possibly somewhat crude but illustrating. Each person in a family has his/her own characteristics, abilities, personality, desires and behaviour. Such persons can be characterised in accordance with their individual features and behaviour. In this sense, each person could be imagined as a 'variable' that can be directly 'measured'. At the same time, each of these individuals are also characterised by an attribute - the fact that they belong to the same family. The family is not the same as each of the individuals belonging to the family. However, the family and its characteristics are something created by the family members and projects onto (i.e., influences) each of the family members. In this sense, the family is a factor or a construct that cannot be measured directly, but is characterised by the combination of its associations with each family person.
Some people may have stronger associations with their family than the other - in the same way as some variables could be more relevant to a considered construct than the other. The strength of association of the variables with a factor is characterised by factor loadings.
Factors could significantly simplify the analysis through the natural grouping of measured variables into distinct manageable groups, thus enhancing the major distinct features of the model and reducing the total number of variables.
Constructs could be considered in an SEM or GSEM structure to establish causal relationships between them and any other independent or dependent variables.
Typically, factor analyses are essential for the evaluation of survey and questionnaire data, as well as for any other data containing correlated variables and/or multiple entries reflecting some mutual overarching feature(s) or attribute(s) that could be regarded as construct(s).
At ACHSOL, we have exceptional expertise and experience in all types of factor analysis, including justification, validation, description and interpretation of the emerging constructs in a wide variety of research and consulting fields.