### Abstract

Factor analysis is a popular statistical model for analyzing correlation structures among observed variables. It is well known that this model has a rotational indeterminacy. Traditionally, the model parameters are estimated by the maximum likelihood method; then, factor rotation methods are applied to obtain an interpretable factor loading matrix. Recently, several sparse estimation procedures via penalization have been developed. Sparse estimation via penalization is an alternative to the factor rotation; it leads to an interpretable and sufficiently sparse solution. In this paper, we give an overview of several sparse factor analysis models, followed by a discussion of a relation between ordinary factor rotation and penalized maximum likelihood approaches. Then, we introduce a novel analyzing tool wherein a user can select a model that is easy to interpret and also possesses desirable values of goodness-of-fit indices based on the graphical representation of solution path.

Original language | English |
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Pages (from-to) | 229-250 |

Number of pages | 22 |

Journal | Behaviormetrika |

Volume | 44 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2017 |

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### Keywords

- Factor analysis
- Factor rotation
- Graphical tool
- Simplicity
- Sparse estimation

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Clinical Psychology
- Experimental and Cognitive Psychology

### Cite this

*Behaviormetrika*,

*44*(1), 229-250. https://doi.org/10.1007/s41237-016-0007-3