---
title: "Day 12: Stochastic Actor-Oriented Models"
engine: knitr
editor: source
subtitle: "Network change, co-evolution, and what the model can claim"
author: "Shahryar Minhas"
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---

## Is This Actually a SAOM Question? {#route}

A SAOM is designed for panel networks in which actors have opportunities to change outgoing ties between observed waves.

::: {.room-prompt}
Can the substantive process be represented as actors making small tie changes while the network and possibly actor behavior co-evolve?
:::

::: {.bottom-line}
Longitudinal data alone do not make a SAOM appropriate. The actor-oriented micro-step story must be a defensible approximation.
:::

::: {.slide-link}
[Open the walkthrough](day12_saom.html#block-a){.walkthrough-link target="_blank"}
:::

::: {.notes}
Opening question from the walkthrough: do actors plausibly control the outgoing relation, and are the waves meaningful snapshots of the process between them?
:::

## Did Similarity Produce the Relationship? {#political-question}

Or did the relationship make the actors more similar?

- **States:** Do states ally because their security policies already align, or do alliances bring their policies closer?
- **Legislators:** Do legislators collaborate because they already hold similar positions, or does collaboration bring their positions closer?
- **Armed groups:** Do groups cooperate because their strategies already align, or does cooperation lead their strategies to converge?

::: {.bottom-line}
Repeated observations help us see what changed first. They do not record every change between waves, so the model shows patterns consistent with selection or influence rather than proving either process.
:::

::: {.slide-link}
[Read the substantive translation](day12_saom.html#sec-political-question){.walkthrough-link target="_blank"}
:::

::: {.notes}
The key question is whether similarity led actors to form a relationship or whether the relationship led them to become more similar. Time provides useful ordering, but the SAOM still fills in the unobserved changes between waves using its actor-oriented micro-step assumptions. The fitted application remains the s50 friendship and drinking panel, so every reported result must return to those students and waves.
:::

## The Specifications Answer Different Applied Questions {#model-compass}

| Specification | Main question | What we should be able to say |
|---|---|---|
| Network SAOM | Which local tie changes are more attractive to actors? | Reciprocity raises the objective-function score of a specific candidate change |
| Co-evolution SAOM | Are similarity patterns consistent with selection, influence, or both? | Similar peers are selected more often, while influence is weaker or uncertain |
| TERGM comparator | Is change better represented as a network transition distribution? | The prior graph predicts the next graph without assigning every intermediate change to an actor |

::: {.slide-link}
[Use the applied model compass](day12_saom.html#sec-model-compass){.walkthrough-link target="_blank"}
:::

::: {.notes}
The result must name a candidate micro-step for SAOMs. A positive evaluation parameter is not an unconditional probability that a friendship forms.
:::

## Pre-Flight Checks Come Before Fitting {#preflight}

| Data feature | Question to settle before fitting |
|---|---|
| Actor composition | Who was actually present and eligible during each interval? |
| Structural zero | Which particular ties were genuinely impossible, not merely absent? |
| Network change | Is there enough continuity and change to estimate a process? |
| Measurement | Are missingness, behavior ranges, direction, and tie definitions defensible? |

`netify` verifies actor order, direction, and dimensions across the friendship waves before the RSiena array is created.

::: {.bottom-line}
A structural zero removes a particular tie from the possible choices. A composition-change object determines when an actor belongs to the modeled population. Joining or leaving is not a control variable.
:::

::: {.slide-link}
[Run the data checks](day12_saom.html#a2){.walkthrough-link target="_blank"}
:::

::: {.notes}
Use 10 only for a genuinely impossible dyad. Use sienaCompositionChange() for joiners and leavers. The latter changes the risk set across both network and behavior processes.
:::

## The Model Fills the Space Between Waves {#microstep}

Observed:

$$Y(t_1)\qquad\longrightarrow\qquad Y(t_2)$$

Modeled between them:

$$Y^{(0)}\rightarrow Y^{(1)}\rightarrow Y^{(2)}\rightarrow\cdots\rightarrow Y^{(M)}$$

At each micro-step, one actor gets an opportunity to change one outgoing tie or make no change.

::: {.say-it}
The micro-steps are a model-based latent path, not events observed in the data.
:::

::: {.slide-link}
[Walk through a micro-step](day12_saom.html#a3){.walkthrough-link target="_blank"}
:::

::: {.notes}
Tiny-network question: what options does the selected actor have? The model integrates over many possible unobserved paths connecting the observed waves.
:::

## Rate and Evaluation Parameters Do Different Jobs {#rate-evaluation}

:::: {.comparison-row}
::: {.comparison-card}
[Rate function]{.card-title}

How often actors receive opportunities to make a change between waves.
:::
::: {.comparison-card .accent-card}
[Evaluation function]{.card-title}

Which available network state an actor tends to prefer when an opportunity occurs.
:::
::::

::: {.bottom-line}
More opportunities do not imply a preference for more ties. Opportunity and direction of change are separate parts of the model.
:::

::: {.notes}
Key distinction: the rate parameter scales the latent change process; it is not a log-odds evaluation effect describing the attractiveness of a specific toggle.
:::

## The Evaluation Function Scores Candidate States {#objective}

$$f_i(y)=\sum_k \beta_k s_{ki}(y)$$

When actor $i$ has an opportunity, candidate next states receive scores based on statistics such as:

- Outdegree
- Reciprocity
- Transitive triplets
- Covariate-related selection

::: {.room-prompt .compact-prompt}
For a proposed tie $i\rightarrow j$, which statistics change for actor $i$?
:::

::: {.notes}
ERGM connection: both interpretations use a change in a statistic, but the probability model and temporal story differ.
:::

## Estimation Simulates the Missing Path {#estimation}

The panel shows the beginning and end of each interval, not the changes in between. RSiena therefore:

1. Uses the rate function to generate opportunities.
2. Uses the evaluation function to assign probabilities to the available one-step changes.
3. Simulates a complete path to the next observed wave.
4. Checks whether that simulated path produces the kinds of changes seen in the panel.
5. Revises the parameters and tries again.

::: {.bottom-line}
The estimator learns which rate and evaluation parameters make the observed changes typical under the assumed micro-step process.
:::

::: {.slide-link}
[Walk Through SAOM Estimation](day12_saom.html#sec-estimation-roadmap){.walkthrough-link target="_blank"}
:::

## What RSiena Is Solving {#moment-target}

Let $S_{\mathrm{obs}}$ be the selected change statistics in the observed panel and $S_{\mathrm{sim}}(\theta)$ the same statistics after simulating paths with parameters $\theta$.

$$
E_{\theta}\!\left[S_{\mathrm{sim}}(\theta)\right]-S_{\mathrm{obs}}=0
$$

Robbins-Monro stochastic approximation moves $\theta$ to reduce the simulated-minus-observed discrepancy. The final phase holds the estimate fixed and uses further simulations for standard errors and convergence checks.

::: {.mini-caution}
Default SAOM estimation is simulation-based method of moments. It is not maximizing a likelihood. Convergence means the targeted moments match within Monte Carlo error, not that the actor-oriented story has been proven.
:::

## Fit the Smallest Model That Answers the Question {#first-fit}

Start with:

- A density or outdegree effect
- Reciprocity when substantively plausible
- A carefully chosen closure effect
- The focal covariate or behavior mechanism

::: {.say-it}
Do not begin with every effect in the RSiena catalog. Each added statistic changes the actor's choice surface and the convergence problem.
:::

::: {.slide-link}
[Fit the first model](day12_saom.html#b1){.walkthrough-link target="_blank"}
:::

::: {.notes}
QMD: create the effects object and add effects one at a time. `getEffects()` and `includeEffects()` form a readable specification record.
:::

## Convergence Is About Simulated Moments Matching Targets {#convergence}

RSiena adjusts parameters until statistics simulated under the current model align with the observed change statistics.

Inspect:

1. Overall maximum convergence ratio
2. Effect-specific t-ratios for deviations
3. Stability across repeated runs or continued estimation

::: {.bottom-line}
A printed coefficient is not interpretable until the estimation has converged well enough for the simulated moment conditions.
:::

::: {.slide-link}
[Break and repair convergence](day12_saom.html#b2){.walkthrough-link target="_blank"}
:::

::: {.notes}
Deliberately bad run: continue from the previous estimate when appropriate rather than restarting blindly. Adding complexity to a nonconverged model usually makes diagnosis harder.
:::

## What the First Fit Is Describing {#first-fit-process}

Between observed waves, the model represents students as receiving opportunities to reconsider one outgoing friendship nomination. At each opportunity, one nomination can be added, removed, or left unchanged.

:::: {.comparison-row}
::: {.comparison-card style="min-height: 4.6em; padding: 0.55em;"}
[Waves 1 to 2]{.card-title}

About **6.52** opportunities per student
:::
::: {.comparison-card .accent-card style="min-height: 4.6em; padding: 0.55em;"}
[Waves 2 to 3]{.card-title}

About **5.21** opportunities per student
:::
::::

::: {.bottom-line}
These rates are not log odds. They describe opportunities in the fitted process, not the number of friendships each student changed. An opportunity can produce no change, and the same tie can be reconsidered more than once.
:::

::: {.notes}
The first fit models friendship change only. Smoking enters as a fixed wave-1 covariate. The rates suggest somewhat more activity in the first interval, but they are not preference effects like reciprocity or transitivity.
:::

## The First Fit in One Table {#first-fit-results}

Interpret each estimate as a contribution to the score of one proposed micro-change.

| Friendship feature | Estimate (SE) | What the sign says |
|---|---:|---|
| One more outgoing nomination | $-2.78\ (0.16)$ | Additional nominations are less attractive |
| Return a nomination | $2.48\ (0.22)$ | Returning a nomination is more attractive |
| Close one friend-of-friend path | $0.66\ (0.15)$ | Closing a path is more attractive |
| Create one three-cycle | $-0.09\ (0.29)$ | Little evidence of a separate cycle pattern |
| Choose someone with the same baseline smoking | $0.14\ (0.15)$ | Little evidence of a smoking-similarity pattern |

::: {.mini-caution}
Start with the sign and describe the proposed change. Say: "Holding the other modeled features constant, this feature makes the proposed change more or less attractive." Exponentiate only if the relative weight helps.
:::

::: {.notes}
The overall convergence ratio is 0.063. Estimate divided by standard error is a rough uncertainty check. Outdegree, reciprocity, and transitive triplets are clearly separated from zero. Three-cycles and same baseline smoking are not.
:::

## Returned Friendships Carry the Strongest Signal {#first-fit-reciprocity}

Suppose student $i$ is considering nominating student $j$.

:::: {.comparison-row}
::: {.comparison-card style="min-height: 5.2em; padding: 0.6em;"}
[$j$ Does Not Nominate $i$]{.card-title}

Adding $i\rightarrow j$ creates another outgoing nomination but does not create reciprocity.
:::
::: {.comparison-card .accent-card style="min-height: 5.2em; padding: 0.6em;"}
[$j$ Already Nominates $i$]{.card-title}

Adding $i\rightarrow j$ returns the nomination and creates reciprocity.
:::
::::

$$
\exp(2.48)\approx 11.9
$$

::: {.bottom-line}
Holding the other modeled features constant, a proposed nomination that returns an existing nomination receives about twelve times the choice weight of an otherwise comparable nomination that does not.
:::

::: {.notes}
Do not say that students are twelve times more likely to be friends. The actual probability depends on every available action and every included statistic. The comparison is between two candidate micro-steps that differ by one unit of reciprocity.
:::

## Friends of Friends Are More Attractive Candidates {#first-fit-transitivity}

Start with:

$$
\text{Alice}\rightarrow\text{Ben}
\qquad\text{and}\qquad
\text{Ben}\rightarrow\text{Cara}.
$$

If Alice adds a nomination to Cara, the move closes one transitive path:

$$
\text{Alice}\rightarrow\text{Cara}.
$$

$$
\exp(0.66)\approx 1.94
$$

::: {.bottom-line}
Holding the other modeled features constant, closing one friend-of-friend path nearly doubles the choice weight of the proposed nomination. Closing three paths contributes $3(0.66)=1.98$ to its score.
:::

::: {.notes}
This is the fitted transitive-closure pattern. It describes which candidate changes receive more weight under the model. It does not prove that students consciously searched through friends' friendship lists.
:::

## What the First Fit Does Not Show {#first-fit-limits}

:::: {.comparison-row}
::: {.comparison-card style="min-height: 5.4em; padding: 0.6em;"}
[Three-Cycles]{.card-title}

Estimate: **-0.09**, SE: **0.29**

No clear evidence of a separate circular pattern such as $i\rightarrow j\rightarrow k\rightarrow i$ after reciprocity and transitivity are included.
:::
::: {.comparison-card .accent-card style="min-height: 5.4em; padding: 0.6em;"}
[Same Baseline Smoking]{.card-title}

Estimate: **0.14**, SE: **0.15**

No clear evidence that students with the same wave-1 smoking status receive more weight as friendship choices after accounting for the network terms.
:::
::::

::: {.bottom-line}
Friendships tend to be returned, and friends of friends tend to become connected. Baseline smoking similarity adds little in this specification. Because smoking is treated as a fixed wave-1 covariate, this model cannot study whether smoking changes with friendships. That requires the co-evolution model next.
:::

::: {.notes}
Do not conclude that smoking and friendship are unrelated. This model uses only baseline smoking as a fixed predictor. It does not represent later smoking changes or estimate peer influence.
:::

## One Proposed Nomination Changes Several Statistics {#coefficient}

Before Alice's decision:

$$
\text{Alice}\rightarrow\text{Ben}\rightarrow\text{Cara},
\qquad
\text{Alice}\rightarrow\text{Elena}\rightarrow\text{Cara},
\qquad
\text{Cara}\rightarrow\text{Alice}.
$$

Adding $\text{Alice}\rightarrow\text{Cara}$ produces:

| Feature | Change | Estimate | Contribution to Alice's score |
|---|---:|---:|---:|
| One more outgoing nomination | $1$ | $-2.78$ | $-2.78$ |
| Returned nomination | $1$ | $2.48$ | $+2.48$ |
| Friend-of-friend paths closed | $2$ | $0.66$ | $+1.32$ |
| **Combined change** |  |  | **$+1.02$** |

::: {.mini-caution}
A total of 1.02 means 2.77 times the weight of making no change, not a tie probability. The model separates contributions to its score, not Alice's reason for the nomination.
:::

::: {.slide-link}
[Work through the combined calculation](day12_saom.html#b3){.walkthrough-link target="_blank"}
:::

::: {.notes}
This slide completes the interpretation sequence after the separate reciprocity and transitivity examples. If the two patterns nearly always occur together, their separate estimates will be less precise.
:::

## Interpret the Same-Smoking Coefficient {#simulated-first-difference}

The smoking comparison is a 0-to-1 change:

| Same-smoking indicator | Meaning |
|---|---|
| $0$ | The two students report different smoking categories |
| $1$ | The two students report the same smoking category |

The estimated same-smoking coefficient is $0.14$:

$$\exp(0.14)=1.15.$$

::: {.bottom-line}
At a modeled friendship-change opportunity, a nomination to a student with the **same smoking status is about 15% more likely to be chosen** than an otherwise identical nomination to a student with a different smoking status.
:::

::: {.mini-caution}
This is a conditional probability ratio between two possible nominations. The estimate is 0.14 with SE 0.15, so the difference is uncertain.
:::

::: {.slide-link}
[Walk through the 0-to-1 comparison](day12_saom.html#smoke-coefficient){.walkthrough-link target="_blank"}
:::

::: {.notes}
Name the variable first. The same-smoking indicator changes from zero for different smoking categories to one for the same category. The coefficient changes the log probability ratio by 0.14, and exponentiating gives a probability ratio of 1.15. Say “15% more likely to be chosen at the modeled opportunity,” not “15 percentage points more likely” and not “the probability of friendship is 15%.”
:::

## One Pattern, Two Possible Histories {#coevolution}

At the final wave, Alice and Cara are friends and report similar drinking. That endpoint alone does not tell us how they got there.

:::: {.comparison-row}
::: {.comparison-card}
[Selection]{.card-title}

They reported similar drinking first, and the friendship appeared later.
:::
::: {.comparison-card .accent-card}
[Influence]{.card-title}

They were friends first, and their reported drinking became more similar later.
:::
::::

::: {.bottom-line}
Several waves give us information about sequence, but we still do not observe every friendship and behavior change between interviews. The model supplies a particular account of that missing path.
:::

## The Co-Evolution Model Uses Two Equations {#coevolution-equations}

Both friendship and drinking now change. Each has its own rates and evaluation equation.

| Equation | Other included terms | Focal term and estimate (SE) |
|---|---|---:|
| **Friendship** | Outdegree, reciprocity, transitive triplets, three-cycles, drinking ego, and drinking alter | Similarity in reported drinking (1 to 5): $1.44\ (0.61)$ |
| **Drinking** | Baseline movement across the 1-to-5 scale and toward the middle or extremes | Movement toward friends' average drinking: $1.36\ (0.95)$ |

The two baseline drinking terms are called **linear shape** and **quadratic shape** in RSiena. They describe where drinking tends to move even apart from friends. They are not time trends.

**Friendship opportunity:** Change one outgoing nomination or make no change. **Drinking opportunity:** Move one category up or down or make no change. Separate period-specific rates govern how often the opportunities arise.

::: {.say-it}
The fitted friendship process favors students with more similar drinking as possible friends. The estimated movement toward friends' drinking is positive, but too uncertain to distinguish from no influence.
:::

::: {.slide-link}
[Build the co-evolution model](day12_saom.html#c1){.walkthrough-link target="_blank"}
:::

::: {.notes}
This is not the smoking model from two slides ago. Drinking now changes endogenously alongside friendship. Selection belongs in the friendship equation, while influence belongs in the drinking equation. The two baseline drinking terms are conventionally called linear shape and quadratic shape. They describe where drinking tends to move even apart from friends. They are not linear and quadratic time trends.
:::

## Interpret the Drinking-Similarity Coefficient {#selection-interpretation}

Reported drinking is coded **1 = none**, **2 = once or twice a year**, **3 = monthly**, **4 = weekly**, and **5 = more than weekly**. RSiena turns the gap into a similarity score:

| Difference in reported drinking | Similarity score |
|---|---:|
| Same category | 1.00 |
| One category apart | 0.75 |
| Two categories apart | 0.50 |

Moving one category closer raises similarity by $0.25$. With the estimated coefficient of $1.44$:

$$0.25 \times 1.44 = 0.36,\qquad \exp(0.36)=1.43.$$

::: {.bottom-line}
At a modeled friendship-change opportunity, a student who is **one drinking category closer is about 43% more likely to be chosen** than an otherwise comparable student.
:::

::: {.slide-link}
[Walk through the coefficient step by step](day12_saom.html#selection-interpretation){.walkthrough-link target="_blank"}
:::

::: {.notes}
Start with the comparison, not the formula. Ask students to imagine two otherwise comparable possible friends. If one candidate is one drinking category closer to the student, that candidate receives 1.43 times the relative choice weight. This is the closest analogue to saying what a one-unit predictor change does. It is not a fixed percentage-point change because the probability of choosing one nomination also depends on every other available nomination, deletion, and the option of no change.
:::

## Put the Influence Result on the Drinking Scale {#influence-first-difference}

Compare the complete joint model with its average-friend influence coefficient at 1.36 against the same model with only that coefficient set to 0. The friendship equation, selection term, drinking shape terms, rates, and starting observations remain fixed.

For students who start with at least one friend and differ from their friends' average, a smaller next-wave distance from that starting friend average means closer.

| Influence coefficient set to 0 | Influence coefficient set to 1.36 | Change from including the term |
|---:|---:|---:|
| 0.88 categories | 0.82 categories | **−0.06 categories** |

::: {.bottom-line}
Within this specification, including the fitted influence term reduces the simulated distance to current friends' starting average by about 0.06 response categories.
:::

::: {.mini-caution}
The influence estimate is 1.36 with SE 0.95. This small point-estimate contrast is not clear evidence of influence.
:::

::: {.slide-link}
[Walk through the influence calculation](day12_saom.html#average-first-differences){.walkthrough-link target="_blank"}
:::

::: {.notes}
“Reports higher drinking” is the wrong outcome because movement toward friends can run upward or downward. This distance measure respects both directions. It is the SAOM analogue of a model-based outcome contrast, but it remains a term-ablation summary rather than a causal effect. Parameter uncertainty is not included on this slide.
:::

## Separate Equations Are Not Automatic Proof {#honest}

| Possible problem | What it could look like here |
|---|---|
| An omitted common cause | A new peer group or family change affects both friendship and drinking |
| Unknown ordering within a wave interval | A friendship and drinking change both occur between interviews |
| Measurement error | A student omits a friendship nomination or reports drinking imprecisely |
| A poor timing model | The meaningful changes happen much faster or more slowly than the interview spacing |

::: {.bottom-line}
The two equations let us represent selection and influence separately. A causal claim still requires a defensible design, timing assumptions, measurement, and model specification.
:::

::: {.notes}
Causal guardrail before interpretation: a SAOM is not an automatic solution to the reflection problem or latent homophily.
:::

## Goodness-of-Fit Asks What the Model Missed {#gof}

After fitting, simulate friendship and drinking histories from the model and compare features that were not directly forced to match.

| Check | What a miss would point toward | Result |
|---|---|---:|
| Number of nominations received | Missing differences in popularity | $p=.589$ |
| Distribution of drinking | A poor model of behavior change | $p=.912$ |
| Types of three-person configurations | Missing closure, cycles, or subgroup structure | **$p=.007$** |

::: {.bottom-line}
The model reproduces the broad popularity and drinking distributions, but not the local three-person patterns. Convergence told us estimation finished. This comparison tells us the fitted model still leaves important network structure unexplained.
:::

::: {.slide-link}
[Run the goodness-of-fit checks](day12_saom.html#c2){.walkthrough-link target="_blank"}
:::

## A Failed Check Suggests a Revision, Not a Fishing Expedition {#gof-revision}

We tried adding degree-based popularity because unequal popularity can create local clustering.

| Specification | Overall convergence | Triad-census GOF |
|---|---:|---:|
| Original co-evolution model | $0.163$ | $p=.007$ |
| Added popularity effect | $0.266$ | $p=.004$ |

::: {.bottom-line}
The revised fit did not converge adequately and did not improve the triad check. We cannot call it a successful repair. The next step is to obtain convergence, rerun the check, and consider a theoretically motivated alternative. It is not to keep adding effects until one p-value exceeds .05.
:::

::: {.notes}
GOF question: does the fitted process reproduce claim-relevant network features beyond the statistics used in estimation?
:::

## A Score Test Temporarily Pins the New Effect at Zero {#score}

We want to know whether indegree popularity belongs in the model. The score test includes that statistic in the calculations but imposes

$$
\beta_{\text{popularity}}=0.
$$

::: {.code-focus}
- `fix = TRUE` keeps the coefficient at zero.
- `initialValue = 0` states the restricted value.
- `test = TRUE` asks whether the model strains against that restriction.
:::

::: {.bottom-line}
RSiena compares the observed popularity-related change with what the restricted model simulates. A large mismatch means the coefficient appears to want to move away from zero.
:::

::: {.slide-link}
[Test without fitting](day12_saom.html#c3){.walkthrough-link target="_blank"}
:::

::: {.notes}
The estimated value prints as 0.000 and its standard error as NA because the coefficient was fixed, not estimated. The score concerns the local pressure at zero.
:::

## What the Score Test Tells Us Here {#score-result}

For the indegree-popularity effect:

$$
\chi^2=5.27,\qquad p=.022.
$$

::: {.say-it}
The observed friendship changes contain more popularity-related structure than the restricted model reproduces. Zero does not look adequate for this effect, so a freely estimated popularity term is worth investigating.
:::

It does **not** tell us:

:::: {.columns}
::: {.column width="48%"}

- The coefficient's direction or size
- Its standard error after estimation
- How other coefficients will change
:::
::: {.column width="48%"}

- Whether the expanded model will converge
- Whether goodness-of-fit will improve
:::
::::

::: {.mini-caution}
Use this as a screen. Then fit the expanded model and check convergence, estimates, and goodness-of-fit.
:::

::: {.notes}
Do not interpret the one-sided Z sign substantively. Its sign depends on RSiena's score convention. Estimate the expanded model to learn direction and magnitude.
:::

## Time Heterogeneity Challenges One-Process Stories {#time}

::: {.big-question}
Are the same evaluation parameters plausible between every pair of waves?
:::

Time-varying effects may be needed when:

- Institutions or opportunities change
- The observation intervals differ
- A shock changes the network process
- Behavior scales or compositions shift

::: {.say-it}
A single average parameter can conceal substantively different transition regimes.
:::

::: {.notes}
Time-dummy workflow: statistical evidence and substantive expectations both matter when deciding whether to allow heterogeneity.
:::

## SAOM and TERGM Encode Different Temporal Stories {#dispute}

:::: {.comparison-row}
::: {.comparison-card}
[SAOM]{.card-title}

Actor-oriented micro-steps, rate and evaluation functions, and choices over outgoing ties.
:::
::: {.comparison-card .accent-card}
[TERGM]{.card-title}

A probability model for networks conditional on past networks and covariates.
:::
::::

::: {.bottom-line}
The choice should follow the research question, temporal resolution, actor control, and desired interpretation, not a claim that one family is universally more realistic.
:::

::: {.notes}
Fair version of the dispute: both approaches approximate unobserved change between waves and can fit similar features through different mechanisms.
:::

## The Referee Checklist {#checklist}

Ask of any SAOM application:

1. Why is actor-oriented change defensible for this relation?
2. How were composition, missingness, and structural zeros handled?
3. Did the model converge across effects and repeated runs?
4. Do simulations reproduce relevant network and behavior features?
5. Are selection, influence, and causal language matched to the assumptions?
6. Would a TERGM or relational event model answer a different and possibly better question?

::: {.slide-link}
[Open the full checklist](day12_saom.html#referee){.walkthrough-link target="_blank"}
:::

::: {.notes}
Synthesis and reading checklist. Closing question: which item is most often omitted in applications we know?
:::

## After the Model Runs, Describe What Changed {#after-fit}

- Separate change opportunities in the **rate function** from preferences in the **evaluation function**.
- Interpret an evaluation effect as a comparison among candidate microsteps, not an unconditional tie probability.
- Keep selection in the network equation and influence in the behavior equation.
- Use convergence, repeated runs, and GOF before stating the substantive conclusion.

::: {.say-it}
"Across three observations of 50 Scottish adolescents, the fitted friendship process gives greater weight to reciprocal and transitive friendship states. The drinking-similarity estimate is 1.44 with a standard error of 0.61, which is consistent with selection into friendships with similar peers. The peer-drinking influence estimate is 1.36 with a standard error of 0.95, so this panel does not distinguish the influence pattern from zero."
:::

::: {.slide-link}
[Read the full interpretation guide](day12_saom.html#sec-after-fit){.walkthrough-link target="_blank"}
:::

::: {.notes}
Keep the output tied to the observed actors and action: adolescents, friendship nominations, drinking, three waves, the fitted selection pattern, the uncertain influence pattern, diagnostics, and remaining confounding.
:::

## What to Carry Into Day 13 {#close}

1. A SAOM fills the intervals between panel waves with actor-oriented micro-steps.
2. Rate and evaluation parameters describe opportunities and preferences, not the same quantity.
3. Co-evolution represents selection and influence jointly but does not identify them causally without strong assumptions.
4. Convergence and goodness-of-fit are separate requirements.
5. SAOM and TERGM encode different temporal questions.

::: {.final-claim}
Tomorrow we separate two problems that are often blurred together: interference changes the estimand, while dyadic dependence changes uncertainty.
:::

::: {.notes}
Day 13 bridge: network change models describe an evolving relation; causal network analysis asks how treatment and outcomes interact through a fixed or measured network and how dyadic regressions should be inferentially calibrated.
:::
