What Is a Latent Variable? How to Read It in SPSS and SmartPLS

What Is a Latent Variable

You open your research model and see concepts such as customer satisfaction, service quality, purchase intention, or trust. These concepts exist in theory, but you cannot measure them with one direct instrument. You need several items in the questionnaire to represent them. The concept behind that group of items is called a latent variable, also known as a construct.

For example, customer satisfaction is a latent variable. You might measure it with the observed variables SAT1, SAT2, SAT3, and SAT4. Each observed variable is a statement in the questionnaire, usually answered on a Likert scale. The measurement model checks whether these statements reflect the same underlying concept.

In PLS-SEM, a latent variable is usually shown as a circle or ellipse, while an observed variable is shown as a rectangle. For a reflective construct, the usual interpretation is that the latent variable causes changes in the observed variables. Outer loading, Cronbach's Alpha, composite reliability, AVE, and HTMT are used to assess this part of the model.

You can summarize the idea as follows:

Latent variable = a theoretical concept represented by one or more observed variables

You can read more about the broader context in What is SEM, but when you are working on a quantitative thesis, deal with two things first: identify the constructs in your model and list the variable codes that belong to each construct.

The Role of Latent Variables in Quantitative Research

Latent variables allow you to bring abstract concepts into a model that can be tested with numerical data. Perceived quality, perceived usefulness, and continuance intention are all difficult to measure directly. A properly designed group of observed variables turns them into quantities that can be analyzed.

The first role of a latent variable is to organize the research model. For example, a model might include Perceived Usefulness, Perceived Ease of Use, Attitude, and Intention to Use. Each construct is a latent variable, while PU1, PU2, PEOU1, and INT1 are the corresponding observed variables. In the hypotheses, you test relationships between constructs, such as the effect of Perceived Usefulness on Attitude.

The second role is to reduce dependence on a single item. A statement may be misunderstood by a respondent or contain measurement error. Multiple observed variables allow the model to assess the reliability and validity of the scale as a whole. Adding more variables does not automatically improve a scale. The variables must point to the same concept and have suitable content.

The third role is to separate the measurement component from the structural relationships. In SmartPLS, you assess the measurement model first and then examine the structural model. This two-step process follows the approach of assessing measurement before testing relationships between constructs, as presented in (Anderson and Gerbing, 1988).

If you are deciding between PLS-SEM and CB-SEM, see PLS-SEM and What is CB-SEM. Both approaches can use latent variables, but their estimation methods, analytical objectives, and reported indicators are different.

What Value Makes a Latent Variable Acceptable

The question of how good a latent variable needs to be often comes up when you see a construct in a SmartPLS diagram. A latent variable does not have one single value that determines whether it is acceptable. You assess it through the indicators of the construct, along with its reliability, convergent validity, and discriminant validity.

The table below applies to a reflective measurement model. Read each row together with the context of your topic, the content quality of the scale, and your supervisor's requirements.

A construct can have good outer loadings and still have a low AVE because AVE is calculated at the construct level. Likewise, a high Alpha is not enough to establish discriminant validity. You also need to examine HTMT or the Fornell-Larcker criterion, where the square root of AVE is compared with the correlations between constructs (Fornell and Larcker, 1981).

When you read the literature, do not mix PLS-SEM thresholds with the CFI, TLI, or RMSEA used in CB-SEM. Those fit indices belong to CB-SEM and are discussed in (Hu and Bentler, 1999). They are not substitutes for outer loading, CR, AVE, and HTMT in SmartPLS.

How to Read a Latent Variable in the Output

In SmartPLS 4, after running PLS Algorithm, you will usually open the Outer Loadings, Construct Reliability and Validity, and Discriminant Validity tables. Column names may vary slightly by version or results screen, but the reading logic remains the same.

The following is illustrative output, not the result of a real study. Assume that the construct “Satisfaction” has four observed variables, SAT1 through SAT4.

Read this table from the observed variable up to the construct. SAT1 has an outer loading of 0.812, which means that it has an appropriate relationship with the Satisfaction construct under the reference threshold. SAT2, SAT3, and SAT4 also exceed 0.70. This illustrates how to present the result. It does not provide evidence that your own scale will produce the same result.

Next, move to the Construct Reliability and Validity table. Cronbach's Alpha of 0.884 and Composite Reliability of 0.921 both exceed the commonly used threshold. AVE of 0.746 exceeds 0.50, so the construct's convergent validity in this example is considered acceptable under (Fornell and Larcker, 1981).

Finally, open Discriminant Validity. In the HTMT table, inspect each pair of constructs. If HTMT between Satisfaction and Purchase Intention is 0.78, the value is below 0.85 under the strict threshold in (Henseler et al., 2015). If the two concepts are very close in content, some studies use 0.90, but you need to explain why you selected that reference point.

For your SEM model, prepare a mapping list before running the analysis: construct name, observed variable codes, measurement type, and related hypothesis. This prevents you from placing SAT1 in the wrong construct or connecting the wrong arrow in the diagram.

In SPSS, a latent variable does not appear as an independent data column unless you have created a composite or mean score. A .sav file usually contains columns for SAT1, SAT2, SAT3, and SAT4. You can run Cronbach's Alpha for this group and then calculate a representative score with Transform > Compute Variable if your analytical design requires it. SPSS processes the observed variable columns. It does not automatically build a latent variable in the way SmartPLS does.

What to Do When a Latent Variable Does Not Meet the Threshold

First, check how the model was specified. A low outer loading may result from an incorrect variable code, an unreversed item, text-formatted data, or an item assigned to the wrong construct. Reopen the data file and codebook before deleting anything.

Check the Data and Reverse-Coded Variables

If SAT3 is a reverse-coded variable but still uses its original coding, its correlation with the other items may be low. In SPSS, check Transform > Recode into Different Variables, then use the new variable in the analysis. In SmartPLS, check the column names and make sure the .csv data has been processed before import.

Review the Content and Outer Loading

If the loading is below 0.70, review Cronbach's Alpha, CR, AVE, and the item's content together. Deleting a variable simply because it increases one indicator can remove an important theoretical aspect of the construct. When the loading is clearly low, the item is unsuitable in content, and the results improve consistently, deleting the item may be defensible.

Check Discriminant Validity

If HTMT exceeds the threshold, check whether the two constructs are measuring the same content. Review the wording, the scale source, and the theoretical model. Combining two constructs only because HTMT is high changes the model. You need an argument for that decision rather than making the change just to produce a cleaner results table.

Rerun the Analysis and Keep Notes

After each adjustment, save a new file version and record which variable was removed, why it was removed, and the indicator values before and after the change. EFA or PLS-SEM rarely produces a perfect table on the first run, but the adjustment sequence must be based on both data and theory. If you delete too many variables, the issue may be in the questionnaire design or the way the construct was defined. Running the software again will not solve the underlying problem.

Distinguishing Latent and Observed Variables

What is an observed variable? It is a quantity recorded directly in the data, usually as a column in an SPSS or CSV file. For example, SAT1 might be the response to the statement “I am satisfied with this service,” coded from 1 to 5. In methodological writing, call SAT1 an observed variable or indicator rather than treating it as the entire concept of satisfaction.

A latent variable exists at the conceptual level. It is represented by a group of observed variables. If Satisfaction consists of SAT1 through SAT4, the four codes are indicators, while Satisfaction is the construct. In SmartPLS, you place the construct on the canvas and assign those indicators to it.

The question of how many observed variables are enough also has no fixed answer for every topic. You need enough indicators to cover the content of the concept while avoiding duplicated or redundant variables. For sample size, the rule of 5 to 10 observations per observed variable is often cited in (Hair et al., 2010), but this is a sample-design guideline, not an outer-loading threshold.

In SPSS, you see observed variables as columns and can run Analyze > Scale > Reliability Analysis to check a group of items. In SmartPLS, those columns become indicators attached to a latent variable. If you calculate the mean of SAT1 through SAT4 in SPSS, the result is a composite variable in the data file. It does not change the nature of the four original indicators.

Common Errors

The first error is calling every SPSS column a latent variable. A column coded SAT1, SAT2, or PU3 is usually an observed variable. The construct exists at the conceptual level or is created in SEM software.

The second error is asking how good a latent variable is based only on the number of constructs. The number of constructs depends on your research question and theory. A model with more latent variables is not automatically better than a model with fewer variables.

The third error is bringing CB-SEM thresholds into SmartPLS. Keep the PLS-SEM indicators together: outer loading, Alpha, CR, AVE, HTMT, VIF, R², f², and Q². In PLS-SEM, R² can be interpreted using the levels 0.75, 0.50, and 0.25 according to (Hair et al., 2011), while Q² greater than 0 is used to assess predictive relevance according to (Stone, 1974).

The fourth error is deleting items in batches without keeping a history. When your lecturer asks why SAT2 was removed, you need to answer using its loading, the scale content, and the results from each run.

Frequently asked questions

How are latent variables and observed variables different?

A latent variable is a concept that is not measured directly, such as satisfaction or trust. An observed variable is an indicator recorded through an individual questionnaire statement, such as SAT1, SAT2, or SAT3. A group of observed variables is usually used to represent one latent variable.

How many latent variables are enough?

There is no construct-count threshold that applies to every topic. Assess each construct using outer loading, Cronbach's Alpha, CR, AVE, and HTMT. You also need to make sure that the number of constructs fits the theoretical model and research question.

How many observed variables are enough?

You need enough observed variables to cover the concept and test its reliability. During sample design, the guideline of 5 to 10 observations per observed variable is cited from (Hair et al., 2010). This is not the criterion for deciding whether an item has an acceptable loading.

Where is the latent variable in SPSS?

SPSS mainly displays observed variables as data columns. You can run Alpha for a group of items and calculate a mean score with Transform > Compute Variable, but a latent variable in the SEM sense is specified more explicitly in SmartPLS, AMOS, or other SEM software.

What should I do if outer loading is low?

Check the data, reverse-coded variables, column codes, and indicator assignment first. Then review loading together with Alpha, CR, AVE, and the item's content. Delete a variable only when the decision has methodological and theoretical support, then rerun the model and save the processing history.

How to write this in your thesis: Open your data file, create a mapping table between each latent variable and its observed variables, then check Outer Loadings, Construct Reliability and Validity, and Discriminant Validity in sequence. If you need to run the analysis on your own .sav or .csv file, DoThesis M4 analysis works through this step with you.