STATISTICAL METHOD
Confirmatory Factor Analysis (CFA)
Statistical Consulting for Measurement Models
We test your prespecified factor structure, choosing the estimator for the item scale, reading global fit together with loadings and residuals, and allowing respecification only for a stated reason, then report the model in publication-ready form.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Confirmatory Factor Analysis?
Confirmatory factor analysis is a latent variable method that tests whether a prespecified measurement model, in which theory assigns each item to its factors, reproduces the relations among observed items. It estimates the loadings, residual variances and factor correlations, and judges the model by global fit and by local indicators such as residuals. Because the structure is fixed in advance, it evaluates a hypothesis and does not discover one, which separates it from exploratory factor analysis. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides confirmatory factor analysis within your study design, with the relevant checks, estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is Confirmatory Factor Analysis Appropriate?
A confirmatory model fits a question about whether a stated factor structure holds for a set of items, and these are the situations in which researchers most often ask us to apply or confirm it.
Validating a Published Scale An established instrument is used in a new sample or setting, and its published factor structure must be shown to hold before scale scores are computed and analyzed.
Testing a Theoretical Structure Theory fixes how many factors an instrument measures and which items belong to each, and competing structures, such as one factor or several, need comparing.
Evidence for Scale Validity A manuscript needs structural validity evidence for a multi-factor scale, drawn from loadings, composite reliability and the correlations among its factors.
Reviewing a Completed Analysis A confirmatory model was respecified after the first run, and a reviewer has questioned the changes. Independent Statistical Review audits the specification and each change.
ANALYTICAL APPROACH
How We Apply Confirmatory Factor Analysis
Within the family of Structural & Latent Variable Modeling, measurement model analysis starts from a structure fixed by theory, not by the data.
A Prespecified Structure We fix the factors, the items on each and the identification before looking at fit. A structure revised after inspection becomes exploratory and needs testing in new data, not a fresh claim of confirmation.
Estimator and Item Type Continuous items suit maximum likelihood with robust standard errors, while few-category ordinal items, such as skewed Likert ratings, usually call for WLSMV with estimated item thresholds instead.
Fit, Loadings and Residuals CFA model fit is judged from several indices read with the loadings and standardized residuals, not a single cutoff. A model can fit well globally and still contain weak or poorly specified items.
Correlated Residuals With Reasons A correlated residual is allowed only with a substantive reason, such as shared wording, and reported openly. Modification indices guide the search, but repeated freeing of parameters overfits the sample.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the measurement model is delivered with the estimates, checks and files needed to report and defend it.
Data & Variable Review Item wording and direction, response categories, distributions, missing data and the number of items per factor are reviewed, and the estimator is matched to the item scale before specification.
Method-Specific Checks Identification, convergence, Heywood cases, residuals and the sensitivity of conclusions to the estimator and to rival structures, such as a one-factor or second-order model, are examined.
Statistical Results Standardized and unstandardized factor loadings with confidence intervals, factor correlations, residual variances, global fit indices, and composite reliability or omega from the fitted model.
Publication-Ready Tables & Figures A measurement model diagram, a loading table and a fit table, formatted to APA 7, COSMIN for health measurement instruments or the journal's requirements, ready to insert.
Interpretation The structure is described as supported, partly supported or not supported, with weak items and any respecification flagged as exploratory, and validity claims limited to what the design allows.
Reproducible Analysis Files R scripts using lavaan, Mplus input files, Stata do-files or SAS PROC CALIS programs are provided where applicable, so every loading can be traced and rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
We choose the method by what is already known about the items. CFA needs a stated structure, and these methods fit questions about discovery, consistency or item-level behavior.
01
Exploratory Factor Analysis (EFA)
When the structure is unknown, or an adapted instrument fails to reproduce its published one, EFA learns it, ideally in a different sample from the confirmatory test.
02
Reliability Analysis (Cronbach's Alpha)
When an established scale only needs its internal consistency estimated, a reliability coefficient answers it, though omega from a fitted model suits unequal loadings.
03
Item Response Theory (IRT)
For a screening tool, where accuracy near a cutoff matters most, an item response model shows how much information each item gives at that trait level, beyond one loading.
04
Structural Equation Modeling (SEM)
When the relations among the constructs are also of interest, structural paths are added to a measurement model that has first been shown to be sound.
CASE EXAMPLE
How We Work in Practice
An illustration of how a confirmatory model moves from a planned structure to a reportable, defensible result.
ILLUSTRATIVE EXAMPLE · PATIENT-REPORTED OUTCOMES RESEARCH · UNITED STATES
A clinical research organization's patient-reported outcomes group needed to confirm the published three-domain structure of a 15-item fatigue questionnaire in a new trial population.
The plan, written before the data were fitted, specified three correlated factors with WLSMV, because the five-point items showed floor effects, and named a one-factor model and a two-factor model merging the two closest domains as rivals. The three-factor model fit adequately overall, but two items with overlapping content showed a large residual correlation, and the team wished to free parameters from modification indices. We declined that search, allowed one residual covariance on the grounds of item content, labeled it exploratory, and reported both versions. Replication in the next study was recommended.
Outcome: The team received the loadings with 95% confidence intervals, factor correlations, fit indices for each model, the models with and without the residual covariance, a methods paragraph and the scripts.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Factor Models
Confirmatory factor models are fitted in R, Mplus, Stata or SAS, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Factor Models Across Research Fields
Confirmatory tests of instrument structure are needed wherever scales are developed and reused, each field bringing its own constructs, populations and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher who was not ready to sign off a first confirmatory model and received a rebuilt analysis with clearer interpretation.
“Our first pass at Confirmatory Factor Analysis (CFA) produced output, but I was not comfortable signing it off because of model fit and whether any changes were theoretically defensible. The analysis was rebuilt carefully and the interpretation was much clearer. The final output made the fit statistics and substantive interpretation much easier to defend.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your factor model, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your confirmatory factor analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, the theory behind the structure, the naming of each factor, interpretation and conclusions remain with you, and our statistical interpretation stays within what the estimates support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Confirmatory Factor Analysis
Short answers to what researchers ask before a confirmatory model, from EFA versus CFA and fit indices to confidentiality and the assessment process.
Should I run EFA or CFA on my scale?
CFA tests a structure that theory or earlier work has already specified, whereas EFA is for learning an unknown structure. Fitting both in the same sample tells little, because a structure found by exploration will usually fit the data that produced it. If a scale’s published structure fails to hold, we explore in one sample and confirm the revised model in a separate one.
Which fit indices and cutoffs should I report?
We report chi-square with its degrees of freedom, RMSEA with its confidence interval, CFI, TLI and SRMR, alongside the loadings and standardized residuals. Familiar cutoffs, such as CFI above 0.95, come from simulation studies and are guidance, not rules, since they shift with model size, estimator and the number of items. No single index declares the model acceptable.
Can I use modification indices to improve my CFA fit?
Only with care. A modification index points to a parameter that would reduce misfit, but freeing it because of the number alone fits the model to the sample’s quirks, and the results may not replicate. A change needs a substantive reason, such as shared item wording, must be reported openly as exploratory and should be checked in new data.
Can you review an analysis that has already been completed?
Yes, we can review a completed confirmatory model before submission or a response to reviewers. We check the specification against theory, the estimator against the item scales, how fit was read, each respecification and its justification, and the reporting, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Confirmatory Factor Analysis?
Share your research question, instrument and data. We assess whether a confirmatory model fits your items and confirm the method before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014