A decision-based diagnostic algorithm for nonconvergence and improper solutions in bifactor CFA models: A replicable protocol [Author Accepted Manuscript]

{"Bifactor":[0],"confirmatory":[1],"factor":[2,11],"analysis":[3],"(CFA)":[4],"partitions":[5],"item":[6],"covariation":[7],"into":[8],"a":[9,61],"general":[10],"and":[12,19,51,71,86,97,104,116,128],"domain-specific":[13],"residual":[14],"factors,":[15],"informing":[16],"essential":[17],"unidimensionality":[18],"subscale":[20],"interpretability.":[21],"In":[22],"applied":[23],"work,":[24],"bifactor":[25],"CFA":[26],"is":[27],"disproportionately":[28],"prone":[29],"to":[30,75,101,131],"estimation":[31],"pathologies,":[32],"often":[33],"summarized":[34],"as":[35,55],"\\"the":[36],"model":[37],"did":[38],"not":[39],"converge,\\"":[40],"obscuring":[41],"distinct":[42],"failure":[43],"signatures":[44],"(optimizer":[45],"nonconvergence,":[46],"non-positive-definite":[47],"information":[48],"matrices/undefined":[49],"SEs,":[50],"inadmissible":[52],"estimates":[53],"such":[54],"Heywood":[56],"cases).":[57],"This":[58],"tutorial":[59],"presents":[60],"nine-step,":[62],"decision-based":[63],"diagnostic":[64],"algorithm":[65],"that":[66],"separates":[67],"convergence":[68],"from":[69],"admissibility":[70],"maps":[72],"each":[73],"signature":[74],"required":[76],"checks,":[77],"explicit":[78],"decision":[79,126],"rules,":[80],"prioritized":[81],"remedies":[82],"(including":[83],"repeated-fit":[84],"stability),":[85],"defensible":[87],"alternative-model":[88],"pathways.":[89],"The":[90],"workflow":[91],"uses":[92],"prespecified":[93],"thresholds,":[94],"reporting":[95,129],"templates,":[96],"an":[98],"operational":[99],"flowchart":[100],"support":[102,132],"auditability":[103],"teaching.":[105],"A":[106],"worked":[107],"example":[108],"using":[109],"the":[110,124],"Holzinger–Swineford":[111],"data":[112],"illustrates":[113],"protocol-guided":[114],"diagnosis":[115],"resolution.":[117],"Supplementary":[118],"Material":[119],"provides":[120],"executable":[121],"R":[122],"code,":[123],"expanded":[125],"guide,":[127],"templates":[130],"implementation.":[133]}

Authors

Publication Details

Journal
Psychology Archives
Published
2026-09-21
DOI
https://doi.org/10.23668/psycharchives.22505
Primary Topic
Psychometric Methodologies and Testing
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
preprint

A decision-based diagnostic algorithm for nonconvergence and improper solutions in bifactor CFA models: A replicable protocol [Author Accepted Manuscript]

Mary Poga, Theodoros Kyriazos
Psychology Archives
Psychometric Methodologies and Testing
preprint

A decision-based diagnostic algorithm for nonconvergence and improper solutions in bifactor CFA models: A replicable protocol [Author Accepted Manuscript]

Mary Poga, Theodoros Kyriazos
preprint en

Abstract

Bifactor confirmatory factor analysis (CFA) partitions item covariation into a general factor and domain-specific residual factors, informing essential unidimensionality and subscale interpretability. In applied work, bifactor CFA is disproportionately prone to estimation pathologies, often summarized as "the model did not converge," obscuring distinct failure signatures (optimizer nonconvergence, non-positive-definite information matrices/undefined SEs, and inadmissible estimates such as Heywood cases). This tutorial presents a nine-step, decision-based diagnostic algorithm that separates convergence from admissibility and maps each signature to required checks, explicit decision rules, prioritized remedies (including repeated-fit stability), and defensible alternative-model pathways. The workflow uses prespecified thresholds, reporting templates, and an operational flowchart to support auditability and teaching. A worked example using the Holzinger–Swineford data illustrates protocol-guided diagnosis and resolution. Supplementary Material provides executable R code, the expanded decision guide, and reporting templates to support implementation.

Psychology Archives
Peace, Justice and strong institutions
Psychometric Methodologies and Testing
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.