What Is Partial Least Squares? How to Read PLS-SEM Results

What Is Partial Least Squares

Partial Least Squares, usually abbreviated as PLS, is a method for estimating relationships between variables. It is especially useful when your model contains latent variables measured by multiple observed variables. In a thesis, you will usually see PLS in the term PLS-SEM, meaning Partial Least Squares Structural Equation Modeling. PLS-SEM uses questionnaire data to assess two parts at the same time: the measurement model and the structural model.

You can think of the process as follows. Observed variables such as DT1, DT2, and DT3 measure a latent variable such as service quality. SmartPLS then estimates the effect from one variable to another, for example, the effect of service quality on satisfaction. The output usually includes outer loading, Cronbach's Alpha, Composite Reliability, AVE, HTMT, VIF, path coefficient, R², f², and Q².

A PLS-SEM model can be represented in general form by the following structural equation:

Y = β1X1 + β2X2 + ... + βkXk + ζ

Here, Y is the endogenous variable, X represents the predictor variables, β is the path coefficient, and ζ is the error term. PLS tells you whether an effect exists and how strong the model's explanatory power is for the endogenous variable through R². It also indicates predictive relevance through Q².

If you are new to SmartPLS, you can also read What is PLS-SEM and the SmartPLS topic hub to place this term within the full analysis process.

The Meaning of Partial Least Squares in Quantitative Research

PLS-SEM helps you answer three groups of questions in a thesis. First, does the scale measure the intended concept? This is the measurement model assessment, which includes outer loading, reliability, convergent validity, and discriminant validity.

Second, does the data support the hypotheses in your model? You will examine the path coefficient, t-statistics, p-value, or confidence interval from bootstrapping. For example, H1 may state that service quality has a positive effect on satisfaction. If the path from CLDV to SHL has a positive coefficient and the p-value reaches your chosen level, the data support H1.

Third, how well does the model explain and predict the outcome variable? R² shows the proportion of variation in an endogenous variable explained by the predictors in the model. Q² is used to assess whether the model has predictive relevance for an endogenous construct. PLS-SEM is therefore often selected when a study focuses on explaining variance and making predictions.

PLS-SEM also allows you to work with models containing many latent variables, many observed variables, and mediation or moderation relationships. A complex model does not automatically make PLS the correct choice. You still need to define the theoretical model, measurement approach, and hypotheses before opening SmartPLS.

If you are confusing SEM, CB-SEM, and PLS-SEM, the article What is SEM and the article about the SEM model can help you separate the concepts before you examine the output.

What Values Are Acceptable for Partial Least Squares

There is no single number that determines whether an entire PLS-SEM model is acceptable. You need to assess the measurement model, the structural model, and the significance of each hypothesis in sequence. The table below lists commonly used thresholds together with their sources so you can justify them in your thesis.

These thresholds are reference points, not instructions to delete indicators mechanically. A low outer loading may suggest that an indicator does not represent the construct well, but the decision to remove it also depends on the scale content, CR, AVE, and discriminant validity. Record every adjustment so that you can explain why an indicator was removed when your supervisor asks.

PLS-SEM does not use CFI, TLI, and RMSEA in the same way as CB-SEM. These indices belong to covariance-based model-fit assessment, and the source (Hu and Bentler, 1999) applies only to CB-SEM. Including them in a SmartPLS assessment table without an explanation mixes two different methodological families.

How to Read Partial Least Squares Output

In SmartPLS 4, you usually run the model in two rounds. The first round assesses the measurement model. The second assesses the structural model after the scale reaches an acceptable level. Read the exact table names instead of judging the model only by the green or red colours in the diagram.

Reading the Outer Loadings Table and Scale Quality

The Outer Loadings table shows which latent variable each indicator loads on and the size of that loading. The Construct Reliability and Validity table usually displays Cronbach's Alpha, rho_A, Composite Reliability, and AVE. The Discriminant Validity table may display HTMT and the Fornell-Larcker criterion, depending on your version of SmartPLS 4.

The following is illustrative output, not the result of a real study.

In this illustrative output, every outer loading exceeds 0.7, Composite Reliability exceeds 0.7, and AVE exceeds 0.5. The highest HTMT is 0.781, below 0.85. You still need to inspect the complete HTMT matrix for every pair of constructs rather than reporting only the most favourable number.

Reading the Path Coefficients and R-Square Tables

The Path Coefficients table usually contains the columns Original Sample (O), Sample Mean (M), Standard Deviation (STDEV), T Statistics, and P Values after you run bootstrapping. The Original Sample column is the estimated path coefficient from your sample. A positive or negative sign indicates the direction of the effect.

The table below is also illustrative output.

If these were real results and you selected a 5% significance level, all three paths would have p-values below 0.05. You could then state that the data support the corresponding effects. The illustrative output must not be inserted into Chapter 4 as though it were your own research result.

Next, open R-Square to assess the explanatory power for each endogenous variable. If SHL has an R² of 0.420, the predictors in the model explain 42.0% of the variance in satisfaction. Do not write that the model explains 42.0% of all respondent behaviour, because R² belongs only to the endogenous variable and the dataset being analysed.

What to Do When Partial Least Squares Results Are Not Acceptable

First, identify which index falls outside the reference range and whether it belongs to the measurement model or the structural model. If an outer loading is low, check the variable code, reverse-coded indicators, and data entry. A reverse-coded indicator that has not been recoded can distort the correlations between observed variables.

Next, consider removing a low-loading indicator only when the statistical and substantive reasons support the decision. After each removal, rerun the model and check CR, AVE, HTMT, and the remaining content of the scale. Do not delete several indicators one after another just to make the output turn green, because the resulting scale may lose important content.

If HTMT is high, check whether the two latent variables are measuring the same concept. Review the wording of the indicators, check for data-entry errors, and consider the theoretical basis. Combining two constructs or changing the model is a research decision, not a technical operation to perform simply because one threshold is exceeded.

If VIF is high, check whether the predictor variables overlap in content. With a low R², do not automatically conclude that the model has failed. R² depends on the context, the outcome variable, and the predictors included in the model. Report it honestly, then examine f², Q², and the theoretical meaning of the path.

When a hypothesis is not statistically significant, retain the result and conclude that the hypothesis is not supported. Changing the sign of the data, deleting respondents because they increase the p-value, or rerunning the analysis until significance appears creates an explanation that is difficult to defend.

Distinguishing Partial Least Squares from CB-SEM

PLS-SEM and CB-SEM both belong to the structural equation modeling family, but their objectives and assessment procedures differ. PLS-SEM focuses on explaining variance and predicting endogenous variables. CB-SEM generally focuses on the fit between the observed covariance matrix and the theoretical model.

Choose PLS-SEM when your research question emphasises prediction, your model contains many constructs, or your objective is to explain an endogenous variable in an applied setting. Consider CB-SEM when the study requires a strict test of an established theoretical model and fit indices need to be reported.

Your software choice also affects how you write Chapter 4. SmartPLS does not turn a model without a theoretical basis into a strong model. AMOS also cannot repair a poor questionnaire, missing data, or indicators that measure the wrong concept.

Common Errors

The first error is calling every analysis run in SmartPLS PLS-SEM. You need a measurement model, a structural model, and constructs connected by hypotheses. If you only calculate means for the indicators and run a regression, that is a different procedure.

The second error is reporting only the path coefficient and p-value while ignoring scale quality. The committee may ask why you trust the relationship between two variables when outer loading, AVE, or HTMT has not been assessed.

The third error is using CB-SEM indices by mistake. CFI, TLI, and RMSEA are not the default criteria for deciding that a SmartPLS model is acceptable. Separate the measurement section, the structural section, and the method you actually used.

The fourth error is taking a screenshot of the SmartPLS diagram and placing it in the thesis. The diagram helps readers see the relationships between variables, but it does not replace the result tables. Chapter 4 should include outer loading, reliability, convergent validity, discriminant validity, VIF, R², path coefficients, and the bootstrapping results relevant to your model.

Frequently asked questions

What is Partial Least Squares, and is PLS-SEM the same thing?

Partial Least Squares is an estimation method. PLS-SEM is the use of that method in a structural equation model containing a measurement model and a structural model. In everyday student usage, the two terms are often used almost interchangeably when students talk about running a model in SmartPLS.

What steps are included in running an estimated model analysis in SmartPLS?

Import your .csv data, draw the model, assign indicators to latent variables, run PLS-SEM Algorithm, assess the measurement model, and then run Bootstrapping. If your model requires prediction, you can also examine the Q²-related results or the prediction procedure supported by the version of SmartPLS you are using.

What values are acceptable for PLS-SEM?

There is no single overall score. A model is usually assessed through outer loading, Composite Reliability, AVE, HTMT, VIF, R², f², Q², and the significance of the path coefficient. For example, CR from 0.7, AVE from 0.5, and HTMT below 0.85 are sourced reference thresholds, but you still need to interpret them in relation to your scale and specific model.

Does PLS-SEM require normally distributed data?

PLS-SEM is often selected because it depends less on the normal-distribution assumption than some CB-SEM approaches. That does not mean the data can have incorrect formats, excessive missing values, or unusual respondents and still be analysed without review. You still need to clean the data, check the coding, and explain your treatment decisions before running SmartPLS.

How is PLS-SEM different from linear regression?

Regression usually uses observed variables or composite scores that have already been calculated. PLS-SEM allows you to model latent variables through multiple observed variables and assess the measurement and structural parts simultaneously. If your study contains only already-composite independent and dependent variables, SPSS regression may be more suitable, depending on the research question.

How to write this in your thesis

Open your data file, check the variable names, and redraw your model before running PLS-SEM Algorithm. Then compare each table with the thresholds and sources in this article. If you need to run the analysis on your own .sav or .csv file and learn how to present the results, see the M4 data analysis module.