In order to obtain a fully general -way interaction ANOVA we must also concatenate every additional interaction term in the vector  and then add an intercept term.
ɪn ˈɔːɹdɚ tʊ əbtˈeɪn ɐ fˈʊli dʒˈɛnɚɹəl wˈeɪ ˌɪntɚɹˈækʃən ænˈoʊvə wiː mˈʌst ˈɔːlsoʊ kəŋkˈætənˌeɪt ˈɛvɹi ɐdˈɪʃənəl ˌɪntɚɹˈækʃən tˈɜːm ɪnðə vˈɛktɚ ænd ðˈɛn ˈæd ɐn ˌɪntɚsˈɛpt tˈɜːm.