Factor Analysis in R: Formula, Verified Results, Charts and Interpretation
Factor analysis in R is a reproducible workflow rather than a distinct statistical estimand. Correct analysis requires explicit package functions, correlation type, extraction method, factor count, rotation, missing-data rule, and saved outputs. This guide uses the supplied real-data results, native MathML equations, matching charts, and separate Python, R, SPSS or AMOS, and Excel verification.
The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Horn retained factors = 3 is retained as a distinct supporting quantity for the R factor-analysis workflow; it is not substituted for the primary result.
What Factor Analysis in R measures
The exact estimand and the result this method is allowed to support.
Factor Analysis in R addresses one defined analytical target: Factor analysis in R is a reproducible workflow rather than a distinct statistical estimand. Correct analysis requires explicit package functions, correlation type, extraction method, factor count, rotation, missing-data rule, and saved outputs.
Quantity estimated in this analysis
The r factor-analysis workflow is reconstructed from the exact variables, matrix, model, panel, or resampling design shown below. The primary output is Horn retained factors = 3; PAF iterations = 374 supplies the first supporting check. Horn retained factors = 3 is retained as a distinct supporting quantity for the R factor-analysis workflow; it is not substituted for the primary result.
For Factor Analysis in R, the calculation retains full precision until the final display. That matters because the software reports, spreadsheet formulas, chart labels, and narrative must refer to one identical result rather than separately rounded approximations.
Interpretation that is not permitted
R defaults differ across packages. Calling principal components or using an unreported default rotation cannot be described generically as factor analysis. Package output should not be reconciled with SPSS until the methods and matrices match.
For Factor Analysis in R, this boundary is substantive. A nearby coefficient may share the same data or model, yet it answers a different question. The article therefore names every supporting statistic instead of using broad labels such as “valid,” “good,” or “significant” without the object being evaluated.
When to use Factor Analysis in R
Research scope, neighboring methods, and excluded claims.
Research question answered
The defensible question is whether the R factor-analysis workflow supports the result stated for the declared dataset and analytical specification. It is answered by verify read.csv2 imports the semicolon file correctly, followed by compare psych::fa and lavaan only for equivalent models. The evidence is bounded by Horn retained factors = 3 and its named companion quantities.
For Factor Analysis in R, changing the case set, expert panel, item block, estimator, factor count, rotation, baseline model, bootstrap design, or criterion definition changes the question. Such a change requires a new result rather than a revision of the wording around the old value.
Nearest methods that answer different questions
Factor Analysis in SPSS: R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults.
Exploratory Factor Analysis: EFA is the statistical procedure; this post focuses on implementing and auditing it in R.
These distinctions determine which formula, output table, and chart can legitimately appear in a Factor Analysis in R post.
Real data used for Factor Analysis in R
Variables, coding, sample or panel size, and the role each input plays.
For Factor Analysis in R, the factor-oriented analysis uses 649 complete records and nine ordered variables. TravelAccess is defined as 5 − traveltime so larger values represent easier travel. The correlation matrix, eigenvalues, communalities, loading matrices, rotation output, and simulation cutoffs all preserve the same variable order.
For the R factor-analysis workflow, the data are not merely background. A change in correlation type, standardization, missing-case rule, variable order, or retained dimension count changes the matrix on which Horn retained factors = 3 was obtained.
| Variable | Meaning | Mean | SD | Range | Construct |
|---|---|---|---|---|---|
| G1 | first-period grade | 11.3991 | 2.7453 | 0–19 | Academic Achievement |
| G2 | second-period grade | 11.5701 | 2.9136 | 0–19 | Academic Achievement |
| G3 | final grade | 11.9060 | 3.2307 | 0–19 | Academic Achievement |
| Medu | mother’s education | 2.5146 | 1.1346 | 0–4 | Educational Advantage |
| Fedu | father’s education | 2.3066 | 1.0999 | 0–4 | Educational Advantage |
| TravelAccess | reverse-coded travel accessibility | 3.4314 | 0.7487 | 1–4 | Educational Advantage |
| goout | frequency of going out | 3.1849 | 1.1758 | 1–5 | Social-Alcohol Exposure |
| Dalc | workday alcohol use | 1.5023 | 0.9248 | 1–5 | Social-Alcohol Exposure |
| Walc | weekend alcohol use | 2.2804 | 1.2844 | 1–5 | Social-Alcohol Exposure |
Factor Analysis in R assumptions and design requirements
Six conditions checked before the coefficient or decision rule is interpreted.
1. The imported separator and variable types are correct
This condition determines whether the input object matches the formula. In the current Factor Analysis in R analysis, the check is to verify read.csv2 imports the semicolon file correctly while preserving Horn retained factors = 3.
For Factor Analysis in R, if the condition is not met, the affected matrix, coefficient, cutoff, or path is recomputed from the corrected inputs. The result is not repaired by changing a label or selecting a more favorable software output.
2. The TravelAccess transformation is reproducible
This requirement controls whether the numerical estimate has the interpretation claimed. In the current Factor Analysis in R analysis, the check is to compare psych::fa and lavaan only for equivalent models while preserving PAF iterations = 374.
For Factor Analysis in R, if the condition is not met, the affected matrix, coefficient, cutoff, or path is recomputed from the corrected inputs. The result is not repaired by changing a label or selecting a more favorable software output.
3. The correlation matrix matches the measurement scale
This design condition prevents an attractive coefficient from being attached to the wrong population or model. In the current Factor Analysis in R analysis, the check is to set fm and rotate explicitly while preserving Overall KMO = 0.713439.
For Factor Analysis in R, if the condition is not met, the affected matrix, coefficient, cutoff, or path is recomputed from the corrected inputs. The result is not repaired by changing a label or selecting a more favorable software output.
4. The extraction method is named
This specification rule keeps the software routes numerically comparable. In the current Factor Analysis in R analysis, the check is to record the parallel-analysis quantile and number of simulations while preserving Bartlett chi-square = 3018.238.
For Factor Analysis in R, if the condition is not met, the affected matrix, coefficient, cutoff, or path is recomputed from the corrected inputs. The result is not repaired by changing a label or selecting a more favorable software output.
5. The rotation and factor count are fixed
This diagnostic requirement is checked before a benchmark is applied. In the current Factor Analysis in R analysis, the check is to export the pattern and factor-correlation matrices while preserving TravelAccess communality = 0.096087.
For Factor Analysis in R, if the condition is not met, the affected matrix, coefficient, cutoff, or path is recomputed from the corrected inputs. The result is not repaired by changing a label or selecting a more favorable software output.
6. Random seeds and simulation settings are saved
This final condition governs whether the conclusion can survive replication or sensitivity analysis. In the current Factor Analysis in R analysis, the check is to save session information and package versions while preserving G2 communality = 0.959989.
For Factor Analysis in R, if the condition is not met, the affected matrix, coefficient, cutoff, or path is recomputed from the corrected inputs. The result is not repaired by changing a label or selecting a more favorable software output.
Factor Analysis in R hypotheses or decision rule
The statistical question is stated at the correct level for this method.
Statistical question
The primary question concerns factorability, reproduced variance, loading structure, or component retention as defined by Factor Analysis in R; no universal significance test covers all of those quantities.
For Factor Analysis in R, where inferential tests exist, they are reported separately from descriptive coefficients and retention rules.
Decision for the worked analysis
The calculation yields Horn retained factors = 3. Horn retained factors = 3 is retained as a distinct supporting quantity for the R factor-analysis workflow; it is not substituted for the primary result.
The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Factor Analysis in R formula and worked substitution
Native MathML preserves fractions, roots, summations, matrices, subscripts, and superscripts.
The equation below is the defining mathematical object for Factor Analysis in R. Its symbols are connected to the saved inputs and to Horn retained factors = 3, PAF iterations = 374, Overall KMO = 0.713439, Bartlett chi-square = 3018.238.
R code must distinguish extraction, rotation, and CFA estimation rather than treating them as one command.
The R workflow reproduces the factorability, retention, and confirmatory fit evidence reported in the article.
Symbol and denominator control
Factor analysis in R is a reproducible workflow rather than a distinct statistical estimand. Correct analysis requires explicit package functions, correlation type, extraction method, factor count, rotation, missing-data rule, and saved outputs.
For Factor Analysis in R, the numerator, denominator, matrix order, degrees of freedom, factor count, or panel size shown in the MathML card is retained exactly. A formula from a neighboring method is not substituted even when both produce values on a similar scale.
Full-precision substitution
For Factor Analysis in R, the spreadsheet and software outputs retain unrounded inputs until the final displayed value. The arithmetic is then reconciled with Horn retained factors = 3 and PAF iterations = 374 .
R defaults differ across packages. Calling principal components or using an unreported default rotation cannot be described generically as factor analysis. Package output should not be reconciled with SPSS until the methods and matrices match.
Step-by-step Factor Analysis in R calculation
Every stage is tied to a saved value and a method-specific condition.
The worked calculation follows six operations specific to the R factor-analysis workflow. Each operation produces a quantity used by the next step, so a discrepancy is resolved where it originates rather than hidden by rounding.
Establish the analytical object
Action: Verify read.csv2 imports the semicolon file correctly.
Numerical trace: Horn retained factors = 3; PAF iterations = 374.
Condition: the imported separator and variable types are correct. This step is repeated after any correction to coding, matrix construction, model syntax, rotation, resampling, or expert-rating denominators.
Reconstruct the first required quantity
Action: Compare psych::fa and lavaan only for equivalent models.
Numerical trace: PAF iterations = 374; Overall KMO = 0.713439.
Condition: the TravelAccess transformation is reproducible. This step is repeated after any correction to coding, matrix construction, model syntax, rotation, resampling, or expert-rating denominators.
Verify the companion quantity
Action: Set fm and rotate explicitly.
Numerical trace: Overall KMO = 0.713439; Bartlett chi-square = 3018.238.
Condition: the correlation matrix matches the measurement scale. This step is repeated after any correction to coding, matrix construction, model syntax, rotation, resampling, or expert-rating denominators.
Apply the decision rule
Action: Record the parallel-analysis quantile and number of simulations.
Numerical trace: Bartlett chi-square = 3018.238; TravelAccess communality = 0.096087.
Condition: the extraction method is named. This step is repeated after any correction to coding, matrix construction, model syntax, rotation, resampling, or expert-rating denominators.
Inspect local evidence
Action: Export the pattern and factor-correlation matrices.
Numerical trace: TravelAccess communality = 0.096087; G2 communality = 0.959989.
Condition: the rotation and factor count are fixed. This step is repeated after any correction to coding, matrix construction, model syntax, rotation, resampling, or expert-rating denominators.
Reconcile and report
Action: Save session information and package versions.
Numerical trace: G2 communality = 0.959989; Oblimin G2 dominant loading = -0.983154.
Condition: random seeds and simulation settings are saved. This step is repeated after any correction to coding, matrix construction, model syntax, rotation, resampling, or expert-rating denominators.
Factor Analysis in R results and interpretation
Primary and supporting statistics are kept separate and precisely labeled.
Primary result
Horn retained factors
The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Why the result is internally coherent
Horn retained factors = 3 is retained as a distinct supporting quantity for the R factor-analysis workflow; it is not substituted for the primary result.
PAF iterations = 374 documents simulation or convergence effort rather than substantive magnitude.
For Factor Analysis in R, the two quantities are reported together because one is primary and the other supplies context; neither is renamed as the other.
| Result item | Exact value | Interpretation restricted to this method |
|---|---|---|
| Horn retained factors | 3 | Horn retained factors = 3 is retained as a distinct supporting quantity for the R factor-analysis workflow; it is not substituted for the primary result. |
| PAF iterations | 374 | PAF iterations = 374 documents simulation or convergence effort rather than substantive magnitude. |
| Overall KMO | 0.713439 | Overall KMO = 0.713439 describes the balance between ordinary and partial correlations, so it informs factorability or item adequacy rather than factor retention. |
| Bartlett chi-square | 3018.238 | Bartlett chi-square = 3018.238 is read with its degrees of freedom, estimator, sample size, and p-value; it is not a stand-alone effect size. |
| TravelAccess communality | 0.096087 | TravelAccess communality = 0.096087 is below the .50 captured-variance reference; the judgment applies to the named construct rather than the whole instrument. |
| G2 communality | 0.959989 | G2 communality = 0.959989 is the proportion of that variable’s variance reproduced by the retained common factors, not an instrument reliability coefficient. |
| Oblimin G2 dominant loading | -0.983154 | Oblimin G2 dominant loading = -0.983154 is tied to a named indicator and matrix; its sign, standardization, primary dimension, and cross-coefficients must remain explicit. |
| Eigenvalue 1 | 3.195831 | Eigenvalue 1 = 3.195831 is interpreted in rank order and beside adjacent observed or simulated roots before a retention decision is made. |
| Eigenvalue 2 | 1.817089 | Eigenvalue 2 = 1.817089 is interpreted in rank order and beside adjacent observed or simulated roots before a retention decision is made. |
| Eigenvalue 3 | 1.393698 | Eigenvalue 3 = 1.393698 is interpreted in rank order and beside adjacent observed or simulated roots before a retention decision is made. |
| Eigenvalue 4 | 0.846560 | Eigenvalue 4 = 0.846560 is interpreted in rank order and beside adjacent observed or simulated roots before a retention decision is made. |
| Three-dimension cumulative variance | 71.1846% | Three-dimension cumulative variance = 71.1846% belongs to the declared matrix and retained dimensions and must not be relabeled as model fit. |
| Parallel iterations | 500 | Parallel iterations = 500 documents simulation or convergence effort rather than substantive magnitude. |
| Observed eigenvalue 3 | 1.393698 | Observed eigenvalue 3 = 1.393698 is interpreted in rank order and beside adjacent observed or simulated roots before a retention decision is made. |
Factor Analysis in R in Python
The Python route calculates or reconstructs the exact named result.
The Python workflow uses factor_analyzer, FactorAnalyzer to calculate or extract the R factor-analysis workflow from the declared data and analytical specification. It must reproduce Horn retained factors = 3 and retain PAF iterations = 374 as a separate supporting quantity.
The code is read as an executable analysis, not as a printed answer. Its critical verification is to verify read.csv2 imports the semicolon file correctly; the associated design condition is that the imported separator and variable types are correct. R defaults differ across packages. Calling principal components or using an unreported default rotation cannot be described generically as factor analysis. Package output should not be reconciled with SPSS until the methods and matrices match.
import pandas as pd
import numpy as npdf = pd.read_csv("student-por.csv", sep=";")
df["TravelAccess"] = 5 - df["traveltime"]
vars9 = ["G1","G2","G3","Medu","Fedu","TravelAccess","goout","Dalc","Walc"]
X = df[vars9].dropna()
from factor_analyzer import FactorAnalyzer
fa=FactorAnalyzer(n_factors=3,method="principal",rotation="oblimin")
fa.fit(X)
print("loadings",fa.loadings_)
print("communalities",fa.get_communalities())
print("uniquenesses",fa.get_uniquenesses())
Factor Analysis in R in R
The R route declares package, estimator, extraction, rotation, or resampling settings.
The R route uses psych and the displayed arguments to estimate the R factor-analysis workflow. Package defaults are made explicit because estimator, matrix type, extraction, rotation, baseline, or bootstrap choices can change the result.
R output is reconciled with Horn retained factors = 3 after the analyst compare psych::fa and lavaan only for equivalent models. Agreement is expected only when the case set, variable order, and method settings match the Python and workbook calculations.
d <- read.csv2("student-por.csv")
d$TravelAccess <- 5 - d$traveltime
vars9 <- c("G1","G2","G3","Medu","Fedu","TravelAccess","goout","Dalc","Walc")
X <- d[vars9]
library(psych)
fit <- fa(X,nfactors=3,fm="pa",rotate="oblimin")
print(fit$loadings,cutoff=0); print(fit$communality); print(fit$Phi)Factor Analysis in R in SPSS or AMOS
The procedure is labeled honestly when base SPSS does not expose the coefficient.
The SPSS or AMOS section shows the procedure that is actually available for the R factor-analysis workflow. When base SPSS does not expose the coefficient, the syntax prepares the correct matrix or model and the coefficient is obtained through AMOS, MATRIX operations, or a validated integration rather than by renaming a different test.
The output must identify Horn retained factors = 3 and the settings needed to reproduce it. The software review specifically set fm and rotate explicitly, while preserving the requirement that the correlation matrix matches the measurement scale.
* Prepare the standardized loading, residual-variance, construct-correlation, or expert-rating table required for Factor Analysis in R.
* Use MATRIX, AMOS, or validated R/Python integration when base SPSS does not expose the coefficient.
* Do not rename a different SPSS statistic as Factor Analysis in R.Factor Analysis in R in Excel
The workbook exposes source values, intermediate arithmetic, and the final formula.
The Excel workbook is an arithmetic audit for the R factor-analysis workflow. Named cells retain the inputs, intermediate components, and final formula leading to Horn retained factors = 3; no rounded constant is pasted over a formula cell.
Excel can verify visible calculations and cross-software agreement, but it does not replace estimation, optimization, rotation, or resampling that must occur in statistical software. The workbook therefore focuses on the check to record the parallel-analysis quantile and number of simulations and documents PAF iterations = 374 independently.
Data: 649 rows with documented coding.
Inputs: named cells or ranges required only by Factor Analysis in R.
Calculation: Use the native MathML formula shown above with named ranges for every input
Audit: compare full-precision Excel output with the Python, R, and SPSS/AMOS values.
Decision: reference the exact result and diagnostics; never paste a rounded value over the formula cell.Factor Analysis in R charts and visual diagnostics
Each supplied image is interpreted through its own values and analytical purpose.
Every image below is interpreted as part of the same Factor Analysis in R analysis. The captions identify what the panel contributes, the exact values visible in the result set, and the condition that would invalidate the reading.
01 Factor-Analysis-In-R Primary Metrics
This panel reconciles the headline estimate with its principal supporting values for Factor Analysis in R. Read Horn retained factors = 3 beside PAF iterations = 374; the first quantity is not replaced by the second.
The chart is used to verify read.csv2 imports the semicolon file correctly. Its interpretation remains valid only when the imported separator and variable types are correct. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
02 Factor-Analysis-In-R R Minres Loadings
This panel locates strong, weak, and cross-indicator coefficients in the declared measurement structure for Factor Analysis in R. Read PAF iterations = 374 beside Overall KMO = 0.713439; the first quantity is not replaced by the second.
The chart is used to compare psych::fa and lavaan only for equivalent models. Its interpretation remains valid only when the TravelAccess transformation is reproducible. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
03 Factor-Analysis-In-R Minres Communalities
This panel provides a visual diagnostic tied to the method’s exact decision rule for Factor Analysis in R. Read Overall KMO = 0.713439 beside Bartlett chi-square = 3018.238; the first quantity is not replaced by the second.
The chart is used to set fm and rotate explicitly. Its interpretation remains valid only when the correlation matrix matches the measurement scale. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
04 Factor-Analysis-In-R Off Diagonal Residuals
This panel examines localized discrepancy after the model or factor solution is fitted for Factor Analysis in R. Read Bartlett chi-square = 3018.238 beside TravelAccess communality = 0.096087; the first quantity is not replaced by the second.
The chart is used to record the parallel-analysis quantile and number of simulations. Its interpretation remains valid only when the extraction method is named. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
05 Factor-Analysis-In-R Verified Result Summary
This panel reconciles the headline estimate with its principal supporting values for Factor Analysis in R. Read TravelAccess communality = 0.096087 beside G2 communality = 0.959989; the first quantity is not replaced by the second.
The chart is used to export the pattern and factor-correlation matrices. Its interpretation remains valid only when the rotation and factor count are fixed. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
01 Factor-Analysis-In-R Primary Metrics
This panel reconciles the headline estimate with its principal supporting values for Factor Analysis in R. Read G2 communality = 0.959989 beside Oblimin G2 dominant loading = -0.983154; the first quantity is not replaced by the second.
The chart is used to save session information and package versions. Its interpretation remains valid only when random seeds and simulation settings are saved. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
02 Factor-Analysis-In-R R Minres Loadings
This panel locates strong, weak, and cross-indicator coefficients in the declared measurement structure for Factor Analysis in R. Read Oblimin G2 dominant loading = -0.983154 beside Eigenvalue 1 = 3.195831; the first quantity is not replaced by the second.
The chart is used to verify read.csv2 imports the semicolon file correctly. Its interpretation remains valid only when the imported separator and variable types are correct. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
03 Factor-Analysis-In-R Minres Communalities
This panel provides a visual diagnostic tied to the method’s exact decision rule for Factor Analysis in R. Read Eigenvalue 1 = 3.195831 beside Eigenvalue 2 = 1.817089; the first quantity is not replaced by the second.
The chart is used to compare psych::fa and lavaan only for equivalent models. Its interpretation remains valid only when the TravelAccess transformation is reproducible. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
04 Factor-Analysis-In-R Minres Optimizer Diagnostics
This panel provides a visual diagnostic tied to the method’s exact decision rule for Factor Analysis in R. Read Eigenvalue 2 = 1.817089 beside Eigenvalue 3 = 1.393698; the first quantity is not replaced by the second.
The chart is used to set fm and rotate explicitly. Its interpretation remains valid only when the correlation matrix matches the measurement scale. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
05 Factor-Analysis-In-R Verified Result Summary
This panel reconciles the headline estimate with its principal supporting values for Factor Analysis in R. Read Eigenvalue 3 = 1.393698 beside Eigenvalue 4 = 0.846560; the first quantity is not replaced by the second.
The chart is used to record the parallel-analysis quantile and number of simulations. Its interpretation remains valid only when the extraction method is named. A visual pattern that conflicts with the saved table triggers re-estimation or relabeling of the specific chart, not a broad claim that the method has passed.
Factor Analysis in R verification and sensitivity analysis
Six failure modes are checked against the formula, data, output, and charts.
The following diagnostics are not a general checklist. Each one targets a failure mode that can change the calculation or interpretation of Factor Analysis in R.
1. Verify read.csv2 imports the semicolon file correctly
Begin by verify read.csv2 imports the semicolon file correctly. For the R factor-analysis workflow, this operation directly connects Horn retained factors = 3 with Overall KMO = 0.713439. Horn retained factors = 3 is retained as a distinct supporting quantity for the R factor-analysis workflow; it is not substituted for the primary result.
The governing condition is that the imported separator and variable types are correct. If it fails, the primary coefficient may be attached to the wrong input object. The remedy is to correct the relevant coding, matrix, model, rotation, resampling, or panel denominator and rerun the calculation. This check also prevents confusion with Factor Analysis in SPSS, because R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults.
2. Compare psych::fa and lavaan only for equivalent models
Next, compare psych::fa and lavaan only for equivalent models. For the R factor-analysis workflow, this operation directly connects PAF iterations = 374 with Bartlett chi-square = 3018.238. PAF iterations = 374 documents simulation or convergence effort rather than substantive magnitude.
The governing condition is that the TravelAccess transformation is reproducible. If it fails, the companion statistic may no longer describe the same model or sample. The remedy is to correct the relevant coding, matrix, model, rotation, resampling, or panel denominator and rerun the calculation. This check also prevents confusion with Exploratory Factor Analysis, because EFA is the statistical procedure; this post focuses on implementing and auditing it in R.
3. Set fm and rotate explicitly
The third verification is to set fm and rotate explicitly. For the R factor-analysis workflow, this operation directly connects Overall KMO = 0.713439 with TravelAccess communality = 0.096087. Overall KMO = 0.713439 describes the balance between ordinary and partial correlations, so it informs factorability or item adequacy rather than factor retention.
The governing condition is that the correlation matrix matches the measurement scale. If it fails, the decision boundary can move because the required quantity has changed. The remedy is to correct the relevant coding, matrix, model, rotation, resampling, or panel denominator and rerun the calculation. This check also prevents confusion with SEM in R, because SEM in R uses a prespecified latent and structural model, usually through lavaan, rather than an exploratory loading search.
4. Record the parallel-analysis quantile and number of simulations
After the core arithmetic is stable, record the parallel-analysis quantile and number of simulations. For the R factor-analysis workflow, this operation directly connects Bartlett chi-square = 3018.238 with G2 communality = 0.959989. Bartlett chi-square = 3018.238 is read with its degrees of freedom, estimator, sample size, and p-value; it is not a stand-alone effect size.
The governing condition is that the extraction method is named. If it fails, software agreement can be artificial if unlike definitions are compared. The remedy is to correct the relevant coding, matrix, model, rotation, resampling, or panel denominator and rerun the calculation. This check also prevents confusion with Factor Analysis in SPSS, because R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults.
5. Export the pattern and factor-correlation matrices
A robustness review must export the pattern and factor-correlation matrices. For the R factor-analysis workflow, this operation directly connects TravelAccess communality = 0.096087 with Oblimin G2 dominant loading = -0.983154. TravelAccess communality = 0.096087 is below the .50 captured-variance reference; the judgment applies to the named construct rather than the whole instrument.
The governing condition is that the rotation and factor count are fixed. If it fails, a favorable average can conceal a local failure. The remedy is to correct the relevant coding, matrix, model, rotation, resampling, or panel denominator and rerun the calculation. This check also prevents confusion with Exploratory Factor Analysis, because EFA is the statistical procedure; this post focuses on implementing and auditing it in R.
6. Save session information and package versions
The final reconciliation should save session information and package versions. For the R factor-analysis workflow, this operation directly connects G2 communality = 0.959989 with Eigenvalue 1 = 3.195831. G2 communality = 0.959989 is the proportion of that variable’s variance reproduced by the retained common factors, not an instrument reliability coefficient.
The governing condition is that random seeds and simulation settings are saved. If it fails, the published conclusion can exceed the evidence actually reproduced. The remedy is to correct the relevant coding, matrix, model, rotation, resampling, or panel denominator and rerun the calculation. This check also prevents confusion with SEM in R, because SEM in R uses a prespecified latent and structural model, usually through lavaan, rather than an exploratory loading search.
| # | Verification operation | Condition protected | Saved quantity traced |
|---|---|---|---|
| 1 | verify read.csv2 imports the semicolon file correctly | the imported separator and variable types are correct | Horn retained factors = 3 |
| 2 | compare psych::fa and lavaan only for equivalent models | the TravelAccess transformation is reproducible | PAF iterations = 374 |
| 3 | set fm and rotate explicitly | the correlation matrix matches the measurement scale | Overall KMO = 0.713439 |
| 4 | record the parallel-analysis quantile and number of simulations | the extraction method is named | Bartlett chi-square = 3018.238 |
| 5 | export the pattern and factor-correlation matrices | the rotation and factor count are fixed | TravelAccess communality = 0.096087 |
| 6 | save session information and package versions | random seeds and simulation settings are saved | G2 communality = 0.959989 |
Factor Analysis in R compared with related methods
Differences in estimand, formula, and conclusion determine the correct choice.
Method choice depends on the estimand, model, and data structure. These three comparisons explain why the post uses the Factor Analysis in R formula and output rather than a nearby procedure.
Factor Analysis in SPSS
R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults.
In the current analysis, PAF iterations = 374 remains evidence for the R factor-analysis workflow; it is not relabeled as a Factor Analysis in SPSS result. PAF iterations = 374 documents simulation or convergence effort rather than substantive magnitude.
Exploratory Factor Analysis
EFA is the statistical procedure; this post focuses on implementing and auditing it in R.
In the current analysis, Overall KMO = 0.713439 remains evidence for the R factor-analysis workflow; it is not relabeled as a Exploratory Factor Analysis result. Overall KMO = 0.713439 describes the balance between ordinary and partial correlations, so it informs factorability or item adequacy rather than factor retention.
SEM in R
SEM in R uses a prespecified latent and structural model, usually through lavaan, rather than an exploratory loading search.
In the current analysis, Bartlett chi-square = 3018.238 remains evidence for the R factor-analysis workflow; it is not relabeled as a SEM in R result. Bartlett chi-square = 3018.238 is read with its degrees of freedom, estimator, sample size, and p-value; it is not a stand-alone effect size.
How to report Factor Analysis in R
A complete result paragraph includes the value, analytical object, settings, and limitation.
Results paragraph
Factor Analysis in R was evaluated using the declared data, specification, and software settings. The primary result was Horn retained factors = 3; PAF iterations = 374 and Overall KMO = 0.713439 supplied supporting context. The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
The report then states the limitation explicitly: R defaults differ across packages. Calling principal components or using an unreported default rotation cannot be described generically as factor analysis. Package output should not be reconciled with SPSS until the methods and matrices match.
Settings that must accompany the result
the imported separator and variable types are correct; the TravelAccess transformation is reproducible; the correlation matrix matches the measurement scale; the extraction method is named.
For Factor Analysis in R, these details identify the exact version of the analysis and make cross-software reconciliation possible.
Verification actions retained in the record
verify read.csv2 imports the semicolon file correctly; compare psych::fa and lavaan only for equivalent models; set fm and rotate explicitly; record the parallel-analysis quantile and number of simulations.
The final wording is revised only after those operations reproduce the saved values.
Factor Analysis in R decision scenarios
For Factor Analysis in R, worked conflicts show how the conclusion changes when an input, assumption, or supporting statistic fails.
Boundary-case interpretation: Verify read.csv2 imports the semicolon file correctly
Consider a review in which Horn retained factors = 3 is reproduced but PAF iterations = 374 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to verify read.csv2 imports the semicolon file correctly and verify that the imported separator and variable types are correct.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Factor Analysis in SPSS only for method selection: R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Input-definition sensitivity: Compare psych::fa and lavaan only for equivalent models
Consider a review in which Overall KMO = 0.713439 is reproduced but Bartlett chi-square = 3018.238 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to compare psych::fa and lavaan only for equivalent models and verify that the TravelAccess transformation is reproducible.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Exploratory Factor Analysis only for method selection: EFA is the statistical procedure; this post focuses on implementing and auditing it in R. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Software-definition reconciliation: Set fm and rotate explicitly
Consider a review in which TravelAccess communality = 0.096087 is reproduced but G2 communality = 0.959989 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to set fm and rotate explicitly and verify that the correlation matrix matches the measurement scale.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with SEM in R only for method selection: SEM in R uses a prespecified latent and structural model, usually through lavaan, rather than an exploratory loading search. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Local-chart conflict: Record the parallel-analysis quantile and number of simulations
Consider a review in which Oblimin G2 dominant loading = -0.983154 is reproduced but Eigenvalue 1 = 3.195831 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to record the parallel-analysis quantile and number of simulations and verify that the extraction method is named.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Factor Analysis in SPSS only for method selection: R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Alternative-method challenge: Export the pattern and factor-correlation matrices
Consider a review in which Eigenvalue 2 = 1.817089 is reproduced but Eigenvalue 3 = 1.393698 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to export the pattern and factor-correlation matrices and verify that the rotation and factor count are fixed.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Exploratory Factor Analysis only for method selection: EFA is the statistical procedure; this post focuses on implementing and auditing it in R. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Replication and reporting decision: Save session information and package versions
Consider a review in which Eigenvalue 4 = 0.846560 is reproduced but Three-dimension cumulative variance = 71.1846% is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to save session information and package versions and verify that random seeds and simulation settings are saved.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with SEM in R only for method selection: SEM in R uses a prespecified latent and structural model, usually through lavaan, rather than an exploratory loading search. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Boundary-case interpretation: Verify read.csv2 imports the semicolon file correctly
Consider a review in which Parallel iterations = 500 is reproduced but Observed eigenvalue 3 = 1.393698 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to verify read.csv2 imports the semicolon file correctly and verify that the imported separator and variable types are correct.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Factor Analysis in SPSS only for method selection: R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Input-definition sensitivity: Compare psych::fa and lavaan only for equivalent models
Consider a review in which Horn 95th percentile root 3 = 1.106209 is reproduced but Horn retained factors = 3 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to compare psych::fa and lavaan only for equivalent models and verify that the TravelAccess transformation is reproducible.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Exploratory Factor Analysis only for method selection: EFA is the statistical procedure; this post focuses on implementing and auditing it in R. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Software-definition reconciliation: Set fm and rotate explicitly
Consider a review in which PAF iterations = 374 is reproduced but Overall KMO = 0.713439 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to set fm and rotate explicitly and verify that the correlation matrix matches the measurement scale.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with SEM in R only for method selection: SEM in R uses a prespecified latent and structural model, usually through lavaan, rather than an exploratory loading search. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Local-chart conflict: Record the parallel-analysis quantile and number of simulations
Consider a review in which Bartlett chi-square = 3018.238 is reproduced but TravelAccess communality = 0.096087 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to record the parallel-analysis quantile and number of simulations and verify that the extraction method is named.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Factor Analysis in SPSS only for method selection: R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Alternative-method challenge: Export the pattern and factor-correlation matrices
Consider a review in which G2 communality = 0.959989 is reproduced but Oblimin G2 dominant loading = -0.983154 is not. For the R factor-analysis workflow, the disagreement cannot be settled by averaging the two outputs because they describe different components of the analysis. The first action is to export the pattern and factor-correlation matrices and verify that the rotation and factor count are fixed.
If the discrepancy persists, the analyst identifies whether the cause is coding, matrix construction, model identification, estimator, rotation, baseline definition, resampling, or panel denominator. The result is compared with Exploratory Factor Analysis only for method selection: EFA is the statistical procedure; this post focuses on implementing and auditing it in R. The published conclusion remains The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
Factor Analysis in R downloads and reproducibility files
All linked files belong to the same analysis and remain on onlineinternetcafe.com.
The four files belong to one Factor Analysis in R analysis. Their primary values, variable order, method settings, and chart labels must agree; a mismatch is resolved in the source calculation before the WordPress draft is published.
Factor Analysis in R frequently asked questions
Answers use the worked result and the exact method boundary.
What does Factor Analysis in R measure?
Factor analysis in R is a reproducible workflow rather than a distinct statistical estimand. Correct analysis requires explicit package functions, correlation type, extraction method, factor count, rotation, missing-data rule, and saved outputs.
What is the main result in this Factor Analysis in R analysis?
Horn retained factors = 3. The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.
What does the result not prove?
R defaults differ across packages. Calling principal components or using an unreported default rotation cannot be described generically as factor analysis. Package output should not be reconciled with SPSS until the methods and matrices match.
Which supporting value should be reported with the primary result?
For Factor Analysis in R, pAF iterations = 374 is the first companion quantity. PAF iterations = 374 documents simulation or convergence effort rather than substantive magnitude.
Which assumption is most likely to change the interpretation?
The first requirement is that the imported separator and variable types are correct. The result is recomputed if that condition is not satisfied.
What is the most important numerical verification?
The analyst must verify read.csv2 imports the semicolon file correctly. That operation traces Horn retained factors = 3 to the formula and saved inputs.
Why can software packages disagree on Factor Analysis in R?
Disagreement can arise because the TravelAccess transformation is reproducible or because the packages implement different estimators, matrices, baselines, rotations, standardizations, bootstrap rules, or coefficient definitions. Matching labels alone is not enough.
How is Factor Analysis in R different from Factor Analysis in SPSS?
R exposes scriptable package settings; SPSS offers dialog and syntax workflows with different defaults.
How should a chart be interpreted?
For Factor Analysis in R, each chart is tied to a named output such as Overall KMO = 0.713439. It supports a local calculation or diagnostic and does not replace the full numerical result.
How should Factor Analysis in R be reported?
Report Horn retained factors = 3, the required supporting quantities, sample or panel size, exact method settings, and this qualified conclusion: The audited R workflow uses the nine declared variables, checks KMO and Bartlett, retains three factors through parallel analysis, fits a common-factor solution, and reports pattern, structure, communalities, and residual evidence.