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\title{ Akaike, H. (1987). Factor analysis and AIC. \emph{Psychometrika}, \emph{52}, 317--332. (3852 citations as of 4/1/2106)}

\author{Online comments by Yoshio Takane}



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\date{Psychometric Society, Asheville, NC, July, 2016}



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\frametitle{How Akaike (1987) Came to Be}

In his online comments on Akaike (1987), Yoshio Takane relates the story of how this highly-cited paper came to appear in \emph{Psychometrika}.

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As President-Elect of the Psychometric Society in 1986, Yoshio was given the usual president's discretionary fund of \$1000 to help support the annual meeting to be held in Toronto.

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Yoshio used the discretionary \$1000 to bring Professor Akaike from Japan to the Toronto meeting.



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Ham Bozdogan and Yoshio Takane organized a session for the Toronto meeting on the AIC (Akaike Information Criterion) and its relatives.

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Besides Akaike (1987), this session also included papers from Ham Bozodogan and Stanley Sclove (both of which are highly cited in their own right).

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The then editor of \emph{Psychometrika}, Ivo Molenaar, asked Yoshio and Ham to make a special section in the journal for the papers presented at the Toronto meeting (the issue of September, 1987).

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\frametitle{What Akaike (1987) Does}

Akaike (1987) uses the AIC for determining the number of factors to retain in a factor analysis.

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AIC: -2log(maximized likelihood) + 2(number of parameters)

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This turns out not to be a straightforward application of AIC model selection.

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As the number of factors is increased, improper solutions appear (that is, Heywood cases where negative estimates of unique variances are obtained).

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As Takane discusses in some detail, Akaike suggested an awkward maximum penalized likelihood estimation strategy, where an appended penalty term was used to keep the variance estimates positive.

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Takane also discusses later work that tried to remove some of this initial awkwardness by using what is called the BIC (Bayesian Information Criterion) and the CAIC (Corrected AIC).

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