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Analytica TutorialTutorial: Analyzing a model

This Tutorial page shows you how to do various kinds of sensitivity analysis to see how changes to input assumptions affect the results, including:

Importance analysis
One way parametric analysis
Two-way parametric analysis
Three-way parametric analysis
Pivoting a graph or table over multiple dimensions

Tutorial Video: Analyze a model (6 minutes)

The difference between renting and buying

We use the Rent vs. Buy Analysis model, a modified version of the model that you used in Tutorial: Open a model to browse and Tutorial: Reviewing a model. In this case, however, open the Rent vs. Buy Analysis model by double-clicking the file labeled Rent vs. Buy Analysis.ana. This model is the module called Model that you explored in Tutorial: Reviewing a model with some additional variables to perform uncertainty analysis. First look at the objective node, Difference between buying and renting:

The difference between the two uncertain values is uncertain. It is positive if it costs less to buy, and negative if it costs less rent over the time period.

Importance analysis

Several of the input variables in the Rent vs. Buy Analysis model are uncertain, defined as probability distributions. It's useful to see how much of the uncertainty in the result, in this case the Difference between buying and renting is due to each of these uncertain inputs. Importance analysis is an easy way to do this. Typically, a few key uncertain inputs are responsible for the lion’s share of the uncertainty in the output, while the rest of the inputs have little impact. If so, you can then focus your efforts on getting more precise estimates or building a more detailed model for those few most “important” inputs.

Importance is defined on a relative scale from 0 to 1. An importance value of 0 indicates that the uncertain input variable has no effect on the uncertainty in the output. A importance of 1 implies that you can "blame" all of the uncertainty in the output on that single input. Technically, it computes importance as the Rank correlation (also known as Spearman's correlation) between the output value and each uncertain input, using the RankCorrel function.

We can see that the input Appreciation Rate contributes most of the uncertainty to the Difference between buying and renting.

For more information on how to create an importance variable in your own model see importance analysis and also Scatter plots in Statistics, Sensitivity, and Uncertainty Analysis.

Parametric analysis

Parametric analysis involves varying the value of an input variable to examine its effect on a selected output. It helps you see how an input affects the desired outcome. Since the importance analysis you just did found that Appreciation rate caused most of the uncertainty in Difference between buying and renting, let's start the parametric analysis with that input variable. You want to change the Definition of Appreciation rate’ from a probability distribution to a list of alternative values.

Click the edit button in the toolbar to switch into edit mode. Then you can modify the model: adding and removing nodes, and modifying existing nodes.
Click the key icon to open the Attribute panel
Click the Appreciation rate node to select it
Select Definition from the Attribute dropdown menu to view its definition.

When the Definition attribute is displayed, it shows the Expression popup menu , currently showing a probability distribution. You can press this to show a menu that lets you change the definition to any of these types of expression:

Expression, or mathematical formula
List
List of Labels
Table
Probability table
Distribution
Choice

For now, you want to change the definition of Appreciation rate from a probability distribution to a list. Then you can enter a list of values from -10% to 10%.

Note that the icon on the Expression popup menu has changed to List .

After selecting a list, the definition shows a single cell -- a box -- containing the previous definition -- in this case, a normal distribution Normal(Inflation,3)

Now replace it with a number, say -10:

To add another cell to the list,

Press the Enter key or down arrow key (not the numeric keypad Enter key). The next cell contains -9 (adding 1 to the previous value).
Change its value to -5.
Press Enter again, and it shows 0. The number in the new cell increments the previous cell by the difference between the last two cells, in this case by 5 -- resulting in zero.
Press Enter twice more, and it adds cells with 5 and 10. You can always override the automatic value by typing in something else.

Pivot the graph as follows:

The resulting graph shows the mid value of buying and renting as Appreciation rate varies from -10% to 10%, using the list of values you just entered. You can see that renting and buying costs about the same at an Appreciation rate of -5% per year -- the switchover value. It would be cheaper to rent if the Appreciation rate is less than -5%. And it would be cheaper to buy if it is greater than -5%.

The table shows the values computed for each parameterized value of Appreciation rate. Appreciation rate acts as an index -- that is, a dimension of the table (array) of values in the Costs of buying and renting. You'll learn a lot more about indexes and arrays, a key source of Analytica's flexibility and power, in Tutorial: Arrays.

Two-way parametric analysis

You can extend this parametric sensitivity analysis to two variables. In this cased, let's look at the effects of changing Buying price along with Appreciation rate.

The first cell in this list contains the expression for the previous definition, 140K. Now change this value, and add additional cells, as you did for Appreciation rate.

The Result window displays the variable’s mid value. The Difference between buying and renting variable now shows three curves over Appreciation rate, one for each Buying price. The key shows the value of Buying price for each curve by color.

The graph shows that a $160K home, coupled with an appreciation rate of -2%/year or less, or a $140K home, coupled with an appreciation rate of -6%/year or less, results in renting being cheaper than buying. What is the best buy, a $120K home or a $160K home? That depends on the appreciation rate. If you expect an appreciation rate less than 9% per year, the less expensive home is the better investment. The more expensive home gives a larger return only for an appreciation rate over 9%.

Three-way parametric analysis

So far the Cost of renting has been held constant. What happens if we change that too?

The result has now has three dimensions, Buying price, Buy or rent, and Appreciation rate. It shows two dimension in the graph, Appreciation rate along the X axis, and Buy or rent, in the Key. The third dimension Buying price is shown at the top of the graph as a slicer dimension, currently set to $120K.

Click the diagonal arrows to change the Buying price in the slicer index.

The graph now show the mid value of Costs of buying and renting given that the Buying price equals $160K.

= Pivot a 3-dimensional graph or table

You can pivot the graph (or table) by selecting different variables to show in the X-axis, Key, or Slicer:

This table shows the mid value cost of buying for the parameterized values of Buying Price and Appreciation Rate.

This table confirms that Cost to Rent does not vary with Buying Price or Appreciation rate -- no surprise when you think about it!

You can quit Analytica at this point.

Summary

This page showed several approaches to sensitivity analysis to find out how changes in key variables affect the results. The next page shows you how to create a new Analytica model.

@@ Line 3: / Line 3: @@
 <breadcrumbs>Analytica Tutorial > {{PAGENAME}}</breadcrumbs>
-This Tutorial page shows you how to:
-* Perform importance analysis
-* Perform parametric analysis
-* Set up and compare alternative decisions
-In this Tutorial you will analyze the ''Rent vs. Buy Analysis ''model, a modified version of the model that you used in [[Tutorial: Open a model to browse]] and [[Tutorial: Reviewing a model]]. You will identify its key sources of uncertainty through '''''importance analysis, perform parametric analysis''''', and '''''compare alternative '''''decisions.
+This Tutorial page shows you how to do various kinds of sensitivity analysis to see how changes to input assumptions affect the results, including:
+* Importance analysis
-For instructions on how to open a model, see “Opening the Rent vs. Buy model”. In this case, however, open the ''Rent vs. Buy Analysis ''model by double-clicking the file labeled '''Rent vs. Buy Analysis.ana'''.
+* One way parametric analysis
+* Two-way parametric analysis
+* Three-way parametric analysis
+* Pivoting a graph or table over multiple dimensions
 <br>
@@ Line 22: / Line 21: @@
 __TOC__
+==The difference between renting and buying==
-==Examine the difference between renting and buying==
+We use the ''Rent vs. Buy Analysis ''model, a modified version of the model that you used in [[Tutorial: Open a model to browse]] and [[Tutorial: Reviewing a model]].  In this case, however, open the ''Rent vs. Buy Analysis ''model by double-clicking the file labeled '''Rent vs. Buy Analysis.ana'''. This model is the module called ''Model ''that you explored in [[Tutorial: Reviewing a model]] with some additional variables to perform uncertainty analysis. First look at the objective node, ''Difference between buying and renting'':
-The ''Rent vs. Buy Analysis ''model is the module called ''Model ''that you explored in [[Tutorial: Reviewing a model]] with the addition of nodes to help you understand the importance of the uncertain inputs to the uncertainty in the output.
-In [[Tutorial: Open a model to browse]] you saw that evaluating ''Costs of buying and renting ''produces a graph of two uncertain values. To understand whether it would be financially advantageous to rent or buy, the ''Rent vs. Buy Analysis ''model includes the objective node, ''Difference between buying and renting''.
 :[[File:Chapter 3.1.png]]
-The difference between the two uncertain values is also uncertain. The difference is positive if buying costs less over the time period, and negative if renting costs less over the time period.
+The difference between the two uncertain values is uncertain. It is positive if it costs less to buy, and negative if it costs less rent over the time period.
 :[[File:Chapter 3.3.png]]
 ==Importance analysis==
-In the ''Rent vs. Buy Analysis ''model, as in most complex models, several of the input variables are uncertain.
-It is often useful to understand how much each uncertain input contributes to the uncertainty in the output. Typically, a few key uncertain inputs are responsible for the lion’s share of the uncertainty in the output, while the rest of the inputs have little impact.
+Several of the input variables in the ''Rent vs. Buy Analysis '' model are uncertain, defined as probability distributions.  It's useful to see how much of the uncertainty in the result, in this case the ''Difference between buying and renting'' is due to each of these uncertain inputs.   [[Importance analysis]] is an easy way to do this.  Typically, a few key uncertain inputs are responsible for the lion’s share of the uncertainty in the output, while the rest of the inputs have little impact.  If so,  you can then focus your efforts on getting more precise estimates or building a more detailed model for those few most “important” inputs.
-Analytica’s [[importance analysis]] features can help you understand which uncertain inputs contribute most to the uncertainty in the output. You can then concentrate on getting more precise estimates or building a more detailed model for the one or two most “important” inputs.
 :[[File:Chapter 3.6.png]]
-Analytica defines '''''importance''''' as the [[rank]] order [[correlation]] between the output value and each uncertain input. Each variable’s importance is calculated on a relative scale from 0 to 1. An importance value of 0 indicates that the uncertain input variable has no effect on the uncertainty in the output. A value of 1 implies total correlation, where all of the uncertainty in the output is due to the uncertainty of a single input.
+Importance is defined on a relative scale from 0 to 1. An importance value of 0 indicates that the uncertain input variable has no effect on the uncertainty in the output. A importance of 1 implies that you can "blame" all of the uncertainty in the output on that single input. Technically, it computes importance as the Rank correlation (also known as Spearman's correlation) between the output value and each uncertain input, using the [[RankCorrel]] function.
 :[[File:Chapter 3.6b.png]]
-It is clear in the figure above that the input ''Appreciation Rate'' is contributing most of the uncertainty in the ''Difference between buying and renting''.
+We can see that the input ''Appreciation Rate'' contributes most of the uncertainty to the ''Difference between buying and renting''.
 :[[File:Chapter 3.8.png]]
-For more information about [[importance analysis]] and the steps to create an importance variable in your own model, see [[Scatter plots]] in the [[Statistics, Sensitivity, and Uncertainty Analysis]] chapter of the [[Analytica User Guide]].
+For more information on how to create an importance variable in your own model see [[importance analysis]] and also [[Scatter plots]] in [[Statistics, Sensitivity, and Uncertainty Analysis]].
-==Perform parametric (sensitivity) analysis==
+==Parametric analysis==
-'''''Parametric analysis '''''(also called '''''sensitivity analysis''''') involves varying the value of an input variable to examine its effect on a selected output. Performing sensitivity analysis often provides useful insights into how small changes in input variable values affect the desired outcome.
-Because the [[importance analysis]] in the section “Importance analysis” revealed that ''Appreciation rate ''caused most of the uncertainty in ''Difference between buying and renting, ''you will start the [[parametric analysis]] with that input variable. You will change ''Appreciation rate''’s definition from a probability distribution to a list of alternative values, and analyze the effect on the ''Difference between buying and renting ''output.
+'''Parametric analysis''' involves varying the value of an input variable to examine its effect on a selected output. It helps you see how an input affects the desired outcome.  Since the [[importance analysis]] you just did found that ''Appreciation rate ''caused most of the uncertainty in ''Difference between buying and renting'', let's  start the parametric analysis with that input variable. You want to change the Definition of ''Appreciation rate''’ from a probability distribution to a list of alternative values.
-Before proceeding, click the edit button [[File:Chapter 3.10a.png]] in the toolbar to switch into edit mode. In edit mode you can modify the model: adding and removing nodes, and modifying existing nodes. Then click the key icon [[File:Chapter 3.10b.png]] to open the [[Attribute panel]], then select the ''Appreciation rate ''node, and then select '''Definition '''from the [[Attribute dropdown menu]] to view its definition.
+# Click the edit button [[File:Chapter 3.10a.png]] in the toolbar to switch into edit mode. Then you can modify the model: adding and removing nodes, and modifying existing nodes.
+# Click the key icon [[File:Chapter 3.10b.png]] to open the [[Attribute panel]]
+# Click the ''Appreciation rate ''node to select it
+# Select '''Definition '''from the [[Attribute dropdown menu]] to view its definition.
 :{{Release||4.6|[[File:Chapter 3.10.png]]}}{{Release|5.0||[[File:Chapter 3.10_v5.0.png]]}}
-When the Definition [[attributes|attribute]] is displayed, the [[Expression popup menu]] [[File:Chapter 3.10c.png]] appears.
+When the Definition [[attributes|attribute]] is displayed, it shows the [[Expression popup menu]] [[File:Chapter 3.10c.png]], currently showing a probability distribution. You can press this to show a menu that lets you change the [[definition]] to any of these types of expression:
-Before proceeding, click the [[toolbar|edit tool]] [[File:Chapter 3.10a.png]] to switch to edit mode.
-The [[Expression popup menu]] allows you to change the [[definition]] of a variable to one of several different types of expressions.
-Expression types include:
 * Expression, or mathematical formula [[File:Chapter 3.10d.png]]
 * List [[File:Chapter 3.10e.png]]
@@ Line 77: / Line 67: @@
 * Choice [[File:Chapter 3.10h.png]]
-You will now use [[the Expression popup menu]] to change the definition of ''Appreciation rate'' from a probability distribution to a list. You will redefine ''Appreciation rate'' as a list of alternative values from -10% to 10%.
+For now, you want to change the definition of ''Appreciation rate'' from a probability distribution to a list. Then you can enter a list of  values from -10% to 10%.
 :[[File:Chapter 3.11.png]]
@@ Line 83: / Line 73: @@
 :[[File:Chapter 3.12.png]]
-Note that the icon on the [[Expression popup menu]] changes to indicate that '''List''' [[File:Chapter 3.10e.png]] is selected.
+Note that the icon on the [[Expression popup menu]] has changed to '''List''' [[File:Chapter 3.10e.png]].
-When a definition is first changed to a list, a cell (indicated by a box around it) appears in the definition. The first cell in the list initially contains the expression that was previously in the definition. In this case, you see the expression for a [[normal]] distribution (Normal(Inflation,3)).
+After selecting a list, the definition shows a single cell -- a box -- containing the previous definition -- in this case, a [[normal]] distribution <code>Normal(Inflation,3)</code>
-You will replace the entry with a number and add cells to perform [[parametric analysis]].
+Now replace it with a number, say -10:
 :[[File:Chapter 3.13.png]]
-<tip>In Analytica, you add cells to a list by pressing the main Enter key, not the numeric keypad Enter key.</tip>
+To add another cell to the list,
+* Press the ''Enter'' key or ''down arrow'' key (not the numeric keypad Enter key). The next cell contains -9 (adding 1 to the previous value).
-A new cell appears with the value -9. Change its value to -5. After you have entered two values, as you press ''Enter'' to add a new cell, Analytica automatically fills in the new cell with a value based on the difference between the last two values. You can override the automatic value by typing the desired value.
+* Change its value to -5.
+* Press ''Enter'' again, and it shows 0. The number in the new cell increments the previous cell by the difference between the last two cells, in this case by 5 -- resulting in zero.
+* Press ''Enter'' twice more, and it adds cells with 5 and 10. You can always override the automatic value by typing in something else.
 :[[File:Chapter 3.14.png]]
@@ Line 105: / Line 97: @@
 :[[File:Chapter 3.17.png]]
-The resulting graph shows the [[mid]] value of buying and renting as a function of ''Appreciation rate'', which varies from -10% to 10%, as you just entered.
+The resulting graph shows the [[mid]] value of buying and renting as ''Appreciation rate'' varies from -10% to 10%, using the list of values you just entered. You can see that   renting and buying costs about the same at an ''Appreciation rate'' of -5% per year -- the '''switchover value'''. It would be cheaper to rent if  the ''Appreciation rate'' is less than -5%. And it would be cheaper to buy if it is greater than -5%.
-''Appreciation rate'' is informally called an '''''index''''' because it characterizes a dimension of another variable’s value, in this case, ''Costs of buying and renting''.
+:[[File:Chapter 3.18-updated.png]]
-The graph shows that at an ''Appreciation rate'' of about -5% per year, renting and buying costs the same. If it is less than -5%, it would be better to rent; if it is greater than -5%, it would be better to buy.
+:[[File:Chapter 3.19-updated.png]]
-:[[File:Chapter 3.18-updated.png]]
 The table shows the values computed for each parameterized value of ''Appreciation rate''.
+''Appreciation rate'' acts as an '''''index''''' -- that is, a dimension of the table (array) of values in the ''Costs of buying and renting''. You'll learn a lot more about indexes and arrays, a key source of Analytica's flexibility and power,  in [[Tutorial: Arrays]].
-:[[File:Chapter 3.19-updated.png]]
-==Evaluate alternative decisions==
+== Two-way parametric analysis ==
-Analytica allows you to perform sensitivity analysis on several variables simultaneously.
-In this section, you will change ''Buying price'' to compare results based on alternative decisions. In doing so, you will perform [[parametric analysis]] on both ''Buying price'' and ''Appreciation rate'' at the same time.
+You can extend this parametric sensitivity analysis to two variables. In this cased, let's look at the effects of changing  ''Buying price'' along with ''Appreciation rate''.
 :[[File:Chapter 3.20-updated.png]]
@@ Line 126: / Line 115: @@
 :[[File:Chapter 3.21-updated.png]]
-The first cell in this list contains the expression for the previous definition, 140K. You will change this value, and add additional cells, as you did in previous steps.
+The first cell in this list contains the expression for the previous definition, 140K. Now change this value, and add additional cells, as you did for ''Appreciation rate''.
 :[[File:Chapter 3.22-updated.png]]
@@ Line 132: / Line 121: @@
 :[[File:Chapter 3.23-updated.png]]
-The [[Result window]] appears displaying the variable’s mid value. The ''Difference between buying and renting variable'' is three curves, one for each ''Buying price''. Below the graph is a key to identify each curve.
+The [[Result window]] displays the variable’s mid value. The ''Difference between buying and renting variable'' now shows three curves over  ''Appreciation rate'', one for each ''Buying price''. The key shows the value of ''Buying price'' for each curve by color.
-When you examine the mid value results, you can see that only a $160K home, coupled with an appreciation rate of -2%/year or less, or a $140K home, coupled with an appreciation rate of -6%/year or less, results in renting being cheaper than buying. So, what is the best buy, a 120K home or a 160K home? That depends on what you anticipate the appreciation rate will be. For appreciation rates less than 9% per year, the less expensive home is the better investment. For higher appreciation rates above 9%, the more expensive home provides a larger return.
+The graph shows that a $160K home, coupled with an appreciation rate of -2%/year or less, or a $140K home, coupled with an appreciation rate of -6%/year or less, results in renting being cheaper than buying. What is the best buy, a $120K home or a $160K home? That depends on the appreciation rate. If you expect an appreciation rate less than 9% per year, the less expensive home is the better investment. The more expensive home gives a larger return only for an appreciation rate over 9%.
 :[[File:Chapter 3.24-updated.png]]
-Remember that the cost of renting has been held constant. To further investigate the effect of this, you will examine the Costs of renting and buying node.
+=== Three-way parametric analysis ===
+So far the ''Cost of renting'' has been held constant. What happens if we change that too?
 :[[File:Chapter 3.25-updated.png]]
@@ Line 146: / Line 137: @@
 :[[File:Chapter 3.27-updated.png]]
-The result has three dimensions, ''Buying price, Buy or rent,'' and ''Appreciation rate'', shown in the figure above.
+The result has now has three dimensions, ''Buying price'', ''Buy or rent,'' and ''Appreciation rate''. It shows two dimension in the graph, ''Appreciation rate'' along the X axis, and ''Buy or rent,'' in the Key.  The third dimension ''Buying price'' is shown at the top of the graph as a slicer dimension, currently set to '''$120K'''.
-Because only two dimensions can be shown in the graph, Analytica chooses one value of the third dimension to display, in this case, ''Buying price'' equals '''$120K'''.
+* Click the diagonal arrows to change the ''Buying price'' in the slicer index.
-Use the navigating arrows to display different values of the ''Buying price'' index.
 :[[File:Chapter 3.28-updated.png]]
@@ Line 156: / Line 145: @@
 :[[File:Chapter 3.29-updated.png]]
-The graph changes to show the [[mid]] value of ''Costs of buying and renting'' given that the ''Buying price'' equals '''$160K'''.
+The graph now show the [[mid]] value of ''Costs of buying and renting'' given that the ''Buying price'' equals '''$160K'''.
+=== Pivot a 3-dimensional graph or table ==
+You can pivot the graph (or table) by selecting different variables to show in the X-axis, Key, or Slicer:
 :[[File:Chapter 3.30-updated.png]]
@@ Line 168: / Line 161: @@
 :[[File:Chapter 3.33-updated.png]]
-This table shows that ''Cost to Rent'' does not vary with ''Buying Price'' or ''Appreciation rate''.
+This table confirms that ''Cost to Rent'' does not vary with ''Buying Price'' or ''Appreciation rate'' -- no surprise when you think about it!
 :[[File:Chapter 3.34-updated.png]]
+You can quit Analytica at this point.
 ==Summary==
-In this chapter, you have:
+This page showed several approaches to sensitivity analysis to find out how changes in key variables affect the results.
-* Performed importance analysis.
+The next page shows you how to create a new Analytica model.
-* Performed parametric analysis.
-* Set up and compared alternative decisions.
-The next chapter introduces you to creating a new Analytica model.
-You can quit Analytica at this point.
 ==See Also==